Theorem: define the Abel-sum type sequence by n ----- \ (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s /d \ (n r + n s + r + s) |-- A[n](r, s)| (n p + n s - n + p + s - 1) A[n](r, s) \dr / - -------------------------------------- + ----------------------------------- n + p n + p /d \ (n + r + 1) |-- A[n + 1](r, s)| \dr / + A[n + 1](r, s) - ------------------------------- = 0 n + p (n + 1) (q + n - s + 1) A[n](r, s) - ---------------------------------- + A[n + 1](r, s) q /d \ (n - s + 1) |-- A[n + 1](r, s)| \ds / + ------------------------------- = 0 q and in Maple notation -(n*p+n*s-n+p+s-1)/(n+p)*A[n](r,s)+(n*r+n*s+r+s)/(n+p)*diff(A[n](r,s),r)+A[n+1] (r,s)-(n+r+1)/(n+p)*diff(A[n+1](r,s),r) = 0 -(n+1)*(q+n-s+1)/q*A[n](r,s)+A[n+1](r,s)+(n-s+1)/q*diff(A[n+1](r,s),s) = 0 ------------------------------------------------- This took, 0.137, seconds. -------------------------------------------- Theorem: define the Abel-sum type sequence by n ----- \ 2 (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)^2*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s 2 2 2 2 2 2 2 2 2 - (n p - n p r + n p s - n r s - 3 n p + n r - 2 n s + 2 n p - 2 n p r 2 2 + 2 n p s - 2 n r s + 2 n - 6 n p + 2 n r - 4 n s + p - p r + p s - r s / 2 + 4 n - 3 p + r - 2 s + 2) A[n](r, s) / ((p - r - 1) (n + r + 1) ) + ( / 2 2 2 2 2 2 2 2 2 n p + 2 n p s - n r - 2 n r s - 3 n p - 3 n s + 2 n p + 4 n p s 2 2 2 2 - 2 n r - 4 n r s + 2 n - 6 n p - 6 n s + p + 2 p s - r - 2 r s + 4 n /d \ / 2 - 3 p - 3 s + 2) |-- A[n](r, s)| / ((p - r - 1) (n + r + 1) ) \dr / / / 2 \ 2 2 |d | (n r + n s + 2 n r + 2 n s + r + s) |--- A[n](r, s)| | 2 | \dr / - ------------------------------------------------------ + 2 (n + r + 1) 2 2 2 3 2 2 2 (n p - n r + 2 n p - 2 n p r + p - p r - 2 n - 4 n p - 2 p ) / 2 A[n + 1](r, s) / ((n + r + 1) (n p - n r + p r - r - n + p - 2 r - 1)) / 2 /d \ (2 n p - 2 n r + 2 p - 2 p r - 3 n - 4 p + r + 1) |-- A[n + 1](r, s)| \dr / - ---------------------------------------------------------------------- 2 n p - n r + p r - r - n + p - 2 r - 1 / 2 \ |d | + |--- A[n + 1](r, s)| = 0 | 2 | \dr / 2 2 2 2 (n + 2 n q - 2 n s + q - 2 q s + s + 2 n + 2 q - 2 s + 1) (n + 2 n + 1) A[n](r, s)/((n - s + 1) %1) - 2 2 2 2 (n + 2 n q - 2 n s + q - 2 q s + s + 2 n + 2 q - 2 s + 1) (n + 2 n + 1) 2 /d \ (n + q - s) q A[n + 1](r, s) |-- A[n](r, s)|/((n - s + 1) %1) + ----------------------------- \ds / (n - s + 1) %1 /d \ + |-- A[n + 1](r, s)| \ds / / 2 \ 2 2 |d | (n + n q - 2 n s - q s + s + 2 n + q - 2 s + 1) |--- A[n + 1](r, s)| | 2 | \ds / + ---------------------------------------------------------------------- %1 = 0 2 %1 := 2 n q + 2 q - 2 q s - n + s - 1 and in Maple notation -(n^2*p^2-n^2*p*r+n^2*p*s-n^2*r*s-3*n^2*p+n^2*r-2*n^2*s+2*n*p^2-2*n*p*r+2*n*p*s -2*n*r*s+2*n^2-6*n*p+2*n*r-4*n*s+p^2-p*r+p*s-r*s+4*n-3*p+r-2*s+2)/(p-r-1)/(n+r+ 1)^2*A[n](r,s)+(n^2*p^2+2*n^2*p*s-n^2*r^2-2*n^2*r*s-3*n^2*p-3*n^2*s+2*n*p^2+4*n *p*s-2*n*r^2-4*n*r*s+2*n^2-6*n*p-6*n*s+p^2+2*p*s-r^2-2*r*s+4*n-3*p-3*s+2)/(p-r-\ 1)/(n+r+1)^2*diff(A[n](r,s),r)-(n^2*r+n^2*s+2*n*r+2*n*s+r+s)/(n+r+1)^2*diff( diff(A[n](r,s),r),r)+(n^2*p-n^2*r+2*n*p^2-2*n*p*r+p^3-p^2*r-2*n^2-4*n*p-2*p^2)/ (n+r+1)/(n*p-n*r+p*r-r^2-n+p-2*r-1)*A[n+1](r,s)-(2*n*p-2*n*r+2*p^2-2*p*r-3*n-4* p+r+1)/(n*p-n*r+p*r-r^2-n+p-2*r-1)*diff(A[n+1](r,s),r)+diff(diff(A[n+1](r,s),r) ,r) = 0 (n^2+2*n*q-2*n*s+q^2-2*q*s+s^2+2*n+2*q-2*s+1)*(n^2+2*n+1)/(n-s+1)/(2*n*q+2*q^2-\ 2*q*s-n+s-1)*A[n](r,s)-(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2+2*n+2*q-2*s+1)*(n^2+2*n+1 )/(n-s+1)/(2*n*q+2*q^2-2*q*s-n+s-1)*diff(A[n](r,s),s)+(n+q-s)*q^2/(n-s+1)/(2*n* q+2*q^2-2*q*s-n+s-1)*A[n+1](r,s)+diff(A[n+1](r,s),s)+(n^2+n*q-2*n*s-q*s+s^2+2*n +q-2*s+1)/(2*n*q+2*q^2-2*q*s-n+s-1)*diff(diff(A[n+1](r,s),s),s) = 0 ------------------------------------------------- This took, 0.068, seconds. -------------------------------------------- Theorem: define the Abel-sum type sequence by n ----- \ 3 (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)^3*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s 3 2 2 2 2 2 2 - (p - 2 p r + p s + p r - 2 p r s + r s - 6 p + 7 p r - 5 p s - r / + 5 r s + 11 p - 5 r + 6 s - 6) A[n](r, s) / ((p - r - 1) / 2 4 3 3 2 2 (p r + p s - r - r s - r - s)) + (2 p - 5 p r + 3 p s + 3 p r 2 3 2 4 3 3 2 2 - 9 p r s + p r + 9 p r s - r - 3 r s - 15 p + 27 p r - 18 p s 2 3 2 2 2 - 9 p r + 36 p r s - 3 r - 18 r s + 40 p - 46 p r + 34 p s + 6 r /d \ / 2 2 - 34 r s - 45 p + 24 r - 21 s + 18) |-- A[n](r, s)| / ((p r + p s \dr / / 2 3 2 2 - 2 p r - 2 p r s + r + r s - 3 p r - 3 p s + 3 r + 3 r s + 2 r + 2 s) 3 2 2 3 2 2 (p - r - 1)) - (p + 3 p s - 3 p r - 6 p r s + 2 r + 3 r s - 6 p / 2 \ 2 |d | / 2 - 12 p s + 6 r + 12 r s + 11 p + 11 s - 6) |--- A[n](r, s)| / (p r | 2 | / \dr / 2 2 3 2 2 + p s - 2 p r - 2 p r s + r + r s - 3 p r - 3 p s + 3 r + 3 r s + 2 r / 3 \ |d | 3 2 3 3 2 2 3 + 2 s) + |--- A[n](r, s)| + (n p - 2 n p r + n r + 3 n p | 3 | \dr / 2 2 2 2 4 3 2 2 5 4 - 6 n p r + 3 n p r + 3 n p - 6 n p r + 3 n p r + p - 2 p r 3 2 3 3 2 2 2 3 2 + p r - 5 n p + 5 n r - 15 n p + 15 n p r - 15 n p + 15 n p r 4 3 3 2 2 3 / - 5 p + 5 p r + 6 n + 18 n p + 18 n p + 6 p ) A[n + 1](r, s) / ( / 3 2 2 3 3 3 2 (n + 3 n + 3 n + 1) (p - r - 1) (r + s)) - (3 n p - 9 n p r 3 2 3 3 2 4 2 3 2 2 2 2 3 + 9 n p r - 3 n r + 6 n p - 15 n p r + 9 n p r + 3 n p r 2 4 5 4 3 2 2 3 4 5 - 3 n r + 3 n p - 3 n p r - 9 n p r + 15 n p r - 6 n p r + 3 p r 4 2 3 3 2 4 3 2 3 3 2 2 3 - 9 p r + 9 p r - 3 p r - 18 n p + 36 n p r - 18 n r - 36 n p 2 2 2 3 4 3 2 2 3 + 54 n p r - 18 n r - 15 n p - 12 n p r + 72 n p r - 48 n p r 4 5 4 3 2 2 3 4 3 + 3 n r + 3 p - 30 p r + 54 p r - 30 p r + 3 p r + 34 n p 3 2 2 2 2 2 3 2 - 34 n r + 66 n p - 30 n p r - 36 n r + 12 n p + 96 n p r 2 3 4 3 2 2 3 4 3 - 126 n p r + 18 n r - 21 p + 96 p r - 96 p r + 22 p r - r - 21 n 2 2 2 2 3 2 - 33 n p - 30 n r + 33 n p - 132 n p r + 36 n r + 51 p - 120 p r 2 3 2 2 2 + 54 p r - 6 r - 9 n - 48 n p + 30 n r - 51 p + 54 p r - 12 r + 9 n /d \ / + 19 p - 10 r - 3) |-- A[n + 1](r, s)| / ((n p - n r - n + p - r - 1) \dr / / 2 2 2 3 2 (n + 2 n + 1) (r + s) (p - 2 p r + r - 3 p + 3 r + 2)) + (3 n p 3 3 2 2 3 2 2 2 3 3 - 6 n p r + 3 n r + 3 n p - 9 n p r + 6 n r + 6 n p r 2 2 4 3 2 2 3 4 3 3 - 9 n p r + 3 n r + 3 p r - 6 p r + 3 p r - 12 n p + 12 n r 2 2 2 2 2 3 2 2 - 9 n p - 18 n p r + 27 n r + 6 n p - 36 n p r + 18 n p r 3 3 2 2 3 4 3 2 2 + 12 n r + 6 p r - 27 p r + 24 p r - 3 r + 11 n - 3 n p + 36 n r 2 2 3 2 2 3 2 - 27 n p + 48 n p r + 12 n r + 3 p - 36 p r + 60 p r - 16 r + 15 n 2 2 + 30 n p - 15 p + 60 p r - 30 r - 3 n + 21 p - 24 r - 7) / 2 \ |d | / 3 2 3 3 2 3 3 |--- A[n + 1](r, s)| / ((n p - 2 n p r + n r - 3 n p + 3 n r | 2 | / \dr / 2 2 2 2 2 3 2 2 2 + 3 n p - 6 n p r + 3 n r + 2 n - 9 n p + 9 n r + 3 n p - 6 n p r 2 2 2 2 + 3 n r + 6 n - 9 n p + 9 n r + p - 2 p r + r + 6 n - 3 p + 3 r + 2) (r + s)) - 3 2 2 3 2 2 (n + 3 n r + 3 n r + r + 3 n + 6 n r + 3 r + 3 n + 3 r + 1) / 3 \ |d | / 3 2 |--- A[n + 1](r, s)| / ((n + 3 n + 3 n + 1) (r + s)) = 0 | 3 | / \dr / 6 5 5 4 2 4 4 2 3 3 3 2 - (n + 3 n q - 3 n s + 3 n q - 6 n q s + 3 n s + n q - 3 n q s 3 2 3 3 5 4 4 3 2 3 + 3 n q s - n s + 6 n + 15 n q - 15 n s + 12 n q - 24 n q s 3 2 2 3 2 2 2 2 2 3 4 3 + 12 n s + 3 n q - 9 n q s + 9 n q s - 3 n s + 15 n + 30 n q 3 2 2 2 2 2 3 2 2 - 30 n s + 18 n q - 36 n q s + 18 n s + 3 n q - 9 n q s + 9 n q s 3 3 2 2 2 2 3 - 3 n s + 20 n + 30 n q - 30 n s + 12 n q - 24 n q s + 12 n s + q 2 2 3 2 2 2 - 3 q s + 3 q s - s + 15 n + 15 n q - 15 n s + 3 q - 6 q s + 3 s / 3 2 2 3 2 2 + 6 n + 3 q - 3 s + 1) A[n](r, s) / (3 n q + 6 n q - 9 n q s / 4 3 2 2 4 3 2 2 3 3 + 3 n q - 12 n q s + 9 n q s - 3 q s + 6 q s - 3 q s - 3 n q 2 3 2 4 3 3 3 2 + 9 n q s + 6 n q - 9 n q s + 3 q - 6 q s + 3 q s + n - 6 n q 2 2 2 2 2 3 2 - 3 n s - 6 n q + 12 n q s + 3 n s + 6 q s - 6 q s - s + 3 n 2 2 6 5 - 3 n q - 6 n s - 3 q + 3 q s + 3 s + 3 n - 3 s + 1) + (n + 3 n q 5 4 2 4 4 2 3 3 3 2 3 2 - 3 n s + 3 n q - 6 n q s + 3 n s + n q - 3 n q s + 3 n q s 3 3 5 4 4 3 2 3 3 2 - n s + 6 n + 15 n q - 15 n s + 12 n q - 24 n q s + 12 n s 2 3 2 2 2 2 2 3 4 3 3 + 3 n q - 9 n q s + 9 n q s - 3 n s + 15 n + 30 n q - 30 n s 2 2 2 2 2 3 2 2 3 + 18 n q - 36 n q s + 18 n s + 3 n q - 9 n q s + 9 n q s - 3 n s 3 2 2 2 2 3 2 + 20 n + 30 n q - 30 n s + 12 n q - 24 n q s + 12 n s + q - 3 q s 2 3 2 2 2 + 3 q s - s + 15 n + 15 n q - 15 n s + 3 q - 6 q s + 3 s + 6 n + 3 q /d \ / 4 2 3 3 - 3 s + 1) (2 n + 2 q - 2 s - 1) |-- A[n](r, s)| / (3 n q + 9 n q \ds / / 3 2 2 4 2 3 2 2 2 5 4 - 12 n q s + 9 n q - 27 n q s + 18 n q s + 3 n q - 18 n q s 3 2 2 3 5 4 2 3 3 2 4 4 + 27 n q s - 12 n q s - 3 q s + 9 q s - 9 q s + 3 q s - 3 n q 3 2 3 2 2 2 2 4 2 2 - 6 n q + 12 n q s + 18 n q s - 18 n q s + 6 n q - 18 n q s 3 5 4 2 3 4 4 3 3 + 12 n q s + 3 q - 6 q s + 6 q s - 3 q s + n - 2 n q - 4 n s 2 2 2 2 2 3 2 2 3 - 12 n q + 6 n q s + 6 n s - 12 n q + 24 n q s - 6 n q s - 4 n s 4 3 2 2 3 4 3 2 2 - 3 q + 12 q s - 12 q s + 2 q s + s + 2 n + 6 n q - 6 n s 2 3 2 3 2 - 12 n q s + 6 n s - 3 q + 6 q s - 2 s + 6 n q + 3 q - 6 q s - 2 n 7 6 6 5 2 5 5 2 + q + 2 s - 1) - (n + 4 n q - 4 n s + 6 n q - 12 n q s + 6 n s 4 3 4 2 4 2 4 3 3 4 3 3 + 4 n q - 12 n q s + 12 n q s - 4 n s + n q - 4 n q s 3 2 2 3 3 3 4 6 5 5 4 2 + 6 n q s - 4 n q s + n s + 6 n + 21 n q - 21 n s + 27 n q 4 4 2 3 3 3 2 3 2 3 3 - 54 n q s + 27 n s + 15 n q - 45 n q s + 45 n q s - 15 n s 2 4 2 3 2 2 2 2 3 2 4 5 + 3 n q - 12 n q s + 18 n q s - 12 n q s + 3 n s + 15 n 4 4 3 2 3 3 2 2 3 + 45 n q - 45 n s + 48 n q - 96 n q s + 48 n s + 21 n q 2 2 2 2 2 3 4 3 2 2 - 63 n q s + 63 n q s - 21 n s + 3 n q - 12 n q s + 18 n q s 3 4 4 3 3 2 2 2 - 12 n q s + 3 n s + 20 n + 50 n q - 50 n s + 42 n q - 84 n q s 2 2 3 2 2 3 4 3 + 42 n s + 13 n q - 39 n q s + 39 n q s - 13 n s + q - 4 q s 2 2 3 4 3 2 2 2 + 6 q s - 4 q s + s + 15 n + 30 n q - 30 n s + 18 n q - 36 n q s 2 3 2 2 3 2 2 + 18 n s + 3 q - 9 q s + 9 q s - 3 s + 6 n + 9 n q - 9 n s + 3 q / 2 \ 2 |d | / 4 2 3 3 - 6 q s + 3 s + n + q - s) |--- A[n](r, s)| / (3 n q + 9 n q | 2 | / \ds / 3 2 2 4 2 3 2 2 2 5 4 - 12 n q s + 9 n q - 27 n q s + 18 n q s + 3 n q - 18 n q s 3 2 2 3 5 4 2 3 3 2 4 4 + 27 n q s - 12 n q s - 3 q s + 9 q s - 9 q s + 3 q s - 3 n q 3 2 3 2 2 2 2 4 2 2 - 6 n q + 12 n q s + 18 n q s - 18 n q s + 6 n q - 18 n q s 3 5 4 2 3 4 4 3 3 + 12 n q s + 3 q - 6 q s + 6 q s - 3 q s + n - 2 n q - 4 n s 2 2 2 2 2 3 2 2 3 - 12 n q + 6 n q s + 6 n s - 12 n q + 24 n q s - 6 n q s - 4 n s 4 3 2 2 3 4 3 2 2 - 3 q + 12 q s - 12 q s + 2 q s + s + 2 n + 6 n q - 6 n s 2 3 2 3 2 - 12 n q s + 6 n s - 3 q + 6 q s - 2 s + 6 n q + 3 q - 6 q s - 2 n 2 2 2 3 (n + 2 n q - 2 n s + q - 2 q s + s ) q A[n + 1](r, s) + q + 2 s - 1) + -------------------------------------------------------- %1 (n - s + 1) /d \ 4 3 2 3 2 3 + |-- A[n + 1](r, s)| + (3 n q + 9 n q - 12 n q s + 9 n q \ds / 2 2 2 2 4 3 2 2 3 - 27 n q s + 18 n q s + 3 n q - 18 n q s + 27 n q s - 12 n q s 4 3 2 2 3 4 4 3 3 2 2 - 3 q s + 9 q s - 9 q s + 3 q s - 3 n - 3 n q + 12 n s + 6 n q 2 2 2 3 2 2 3 4 + 9 n q s - 18 n s + 9 n q - 12 n q s - 9 n q s + 12 n s + 3 q 3 2 2 3 4 3 2 2 2 - 9 q s + 6 q s + 3 q s - 3 s - 8 n - 17 n q + 24 n s - 9 n q 2 2 2 3 2 + 34 n q s - 24 n s + 9 q s - 17 q s + 8 s - 6 n - 13 n q + 12 n s / 2 \ 2 2 |d | - 6 q + 13 q s - 6 s - 2 q + 1) |--- A[n + 1](r, s)|/((n + q - s - 1) %1 | 2 | \ds / 5 4 4 3 2 3 3 2 2 3 ) + (n + 3 n q - 5 n s + 3 n q - 12 n q s + 10 n s + n q 2 2 2 2 2 3 3 2 2 3 - 9 n q s + 18 n q s - 10 n s - 2 n q s + 9 n q s - 12 n q s 4 3 2 2 3 4 5 4 3 3 + 5 n s + q s - 3 q s + 3 q s - s + 4 n + 10 n q - 16 n s 2 2 2 2 2 3 2 2 + 8 n q - 30 n q s + 24 n s + 2 n q - 16 n q s + 30 n q s 3 3 2 2 3 4 3 2 2 - 16 n s - 2 q s + 8 q s - 10 q s + 4 s + 6 n + 12 n q - 18 n s 2 2 3 2 2 3 2 + 7 n q - 24 n q s + 18 n s + q - 7 q s + 12 q s - 6 s + 4 n / 3 \ 2 2 |d | + 6 n q - 8 n s + 2 q - 6 q s + 4 s + n + q - s) |--- A[n + 1](r, s)|/( | 3 | \ds / (n + q - s - 1) %1) = 0 2 2 3 2 4 3 2 2 2 2 %1 := 3 n q + 6 n q - 6 n q s + 3 q - 6 q s + 3 q s - 3 n q - 3 n q 2 2 2 2 2 + 6 n q s + 3 q s - 3 q s + n - 3 n q - 2 n s - 3 q + 3 q s + s + 2 n - 2 s + 1 and in Maple notation -(p^3-2*p^2*r+p^2*s+p*r^2-2*p*r*s+r^2*s-6*p^2+7*p*r-5*p*s-r^2+5*r*s+11*p-5*r+6* s-6)/(p-r-1)/(p*r+p*s-r^2-r*s-r-s)*A[n](r,s)+(2*p^4-5*p^3*r+3*p^3*s+3*p^2*r^2-9 *p^2*r*s+p*r^3+9*p*r^2*s-r^4-3*r^3*s-15*p^3+27*p^2*r-18*p^2*s-9*p*r^2+36*p*r*s-\ 3*r^3-18*r^2*s+40*p^2-46*p*r+34*p*s+6*r^2-34*r*s-45*p+24*r-21*s+18)/(p^2*r+p^2* s-2*p*r^2-2*p*r*s+r^3+r^2*s-3*p*r-3*p*s+3*r^2+3*r*s+2*r+2*s)/(p-r-1)*diff(A[n]( r,s),r)-(p^3+3*p^2*s-3*p*r^2-6*p*r*s+2*r^3+3*r^2*s-6*p^2-12*p*s+6*r^2+12*r*s+11 *p+11*s-6)/(p^2*r+p^2*s-2*p*r^2-2*p*r*s+r^3+r^2*s-3*p*r-3*p*s+3*r^2+3*r*s+2*r+2 *s)*diff(diff(A[n](r,s),r),r)+diff(diff(diff(A[n](r,s),r),r),r)+(n^3*p^2-2*n^3* p*r+n^3*r^2+3*n^2*p^3-6*n^2*p^2*r+3*n^2*p*r^2+3*n*p^4-6*n*p^3*r+3*n*p^2*r^2+p^5 -2*p^4*r+p^3*r^2-5*n^3*p+5*n^3*r-15*n^2*p^2+15*n^2*p*r-15*n*p^3+15*n*p^2*r-5*p^ 4+5*p^3*r+6*n^3+18*n^2*p+18*n*p^2+6*p^3)/(n^3+3*n^2+3*n+1)/(p-r-1)^2/(r+s)*A[n+ 1](r,s)-(3*n^3*p^3-9*n^3*p^2*r+9*n^3*p*r^2-3*n^3*r^3+6*n^2*p^4-15*n^2*p^3*r+9*n ^2*p^2*r^2+3*n^2*p*r^3-3*n^2*r^4+3*n*p^5-3*n*p^4*r-9*n*p^3*r^2+15*n*p^2*r^3-6*n *p*r^4+3*p^5*r-9*p^4*r^2+9*p^3*r^3-3*p^2*r^4-18*n^3*p^2+36*n^3*p*r-18*n^3*r^2-\ 36*n^2*p^3+54*n^2*p^2*r-18*n^2*r^3-15*n*p^4-12*n*p^3*r+72*n*p^2*r^2-48*n*p*r^3+ 3*n*r^4+3*p^5-30*p^4*r+54*p^3*r^2-30*p^2*r^3+3*p*r^4+34*n^3*p-34*n^3*r+66*n^2*p ^2-30*n^2*p*r-36*n^2*r^2+12*n*p^3+96*n*p^2*r-126*n*p*r^2+18*n*r^3-21*p^4+96*p^3 *r-96*p^2*r^2+22*p*r^3-r^4-21*n^3-33*n^2*p-30*n^2*r+33*n*p^2-132*n*p*r+36*n*r^2 +51*p^3-120*p^2*r+54*p*r^2-6*r^3-9*n^2-48*n*p+30*n*r-51*p^2+54*p*r-12*r^2+9*n+ 19*p-10*r-3)/(n*p-n*r-n+p-r-1)/(n^2+2*n+1)/(r+s)/(p^2-2*p*r+r^2-3*p+3*r+2)*diff (A[n+1](r,s),r)+(3*n^3*p^2-6*n^3*p*r+3*n^3*r^2+3*n^2*p^3-9*n^2*p*r^2+6*n^2*r^3+ 6*n*p^3*r-9*n*p^2*r^2+3*n*r^4+3*p^3*r^2-6*p^2*r^3+3*p*r^4-12*n^3*p+12*n^3*r-9*n ^2*p^2-18*n^2*p*r+27*n^2*r^2+6*n*p^3-36*n*p^2*r+18*n*p*r^2+12*n*r^3+6*p^3*r-27* p^2*r^2+24*p*r^3-3*r^4+11*n^3-3*n^2*p+36*n^2*r-27*n*p^2+48*n*p*r+12*n*r^2+3*p^3 -36*p^2*r+60*p*r^2-16*r^3+15*n^2+30*n*p-15*p^2+60*p*r-30*r^2-3*n+21*p-24*r-7)/( n^3*p^2-2*n^3*p*r+n^3*r^2-3*n^3*p+3*n^3*r+3*n^2*p^2-6*n^2*p*r+3*n^2*r^2+2*n^3-9 *n^2*p+9*n^2*r+3*n*p^2-6*n*p*r+3*n*r^2+6*n^2-9*n*p+9*n*r+p^2-2*p*r+r^2+6*n-3*p+ 3*r+2)/(r+s)*diff(diff(A[n+1](r,s),r),r)-(n^3+3*n^2*r+3*n*r^2+r^3+3*n^2+6*n*r+3 *r^2+3*n+3*r+1)/(n^3+3*n^2+3*n+1)/(r+s)*diff(diff(diff(A[n+1](r,s),r),r),r) = 0 -(n^6+3*n^5*q-3*n^5*s+3*n^4*q^2-6*n^4*q*s+3*n^4*s^2+n^3*q^3-3*n^3*q^2*s+3*n^3*q *s^2-n^3*s^3+6*n^5+15*n^4*q-15*n^4*s+12*n^3*q^2-24*n^3*q*s+12*n^3*s^2+3*n^2*q^3 -9*n^2*q^2*s+9*n^2*q*s^2-3*n^2*s^3+15*n^4+30*n^3*q-30*n^3*s+18*n^2*q^2-36*n^2*q *s+18*n^2*s^2+3*n*q^3-9*n*q^2*s+9*n*q*s^2-3*n*s^3+20*n^3+30*n^2*q-30*n^2*s+12*n *q^2-24*n*q*s+12*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3+15*n^2+15*n*q-15*n*s+3*q^2-6*q*s +3*s^2+6*n+3*q-3*s+1)/(3*n^3*q^2+6*n^2*q^3-9*n^2*q^2*s+3*n*q^4-12*n*q^3*s+9*n*q ^2*s^2-3*q^4*s+6*q^3*s^2-3*q^2*s^3-3*n^3*q+9*n^2*q*s+6*n*q^3-9*n*q*s^2+3*q^4-6* q^3*s+3*q*s^3+n^3-6*n^2*q-3*n^2*s-6*n*q^2+12*n*q*s+3*n*s^2+6*q^2*s-6*q*s^2-s^3+ 3*n^2-3*n*q-6*n*s-3*q^2+3*q*s+3*s^2+3*n-3*s+1)*A[n](r,s)+(n^6+3*n^5*q-3*n^5*s+3 *n^4*q^2-6*n^4*q*s+3*n^4*s^2+n^3*q^3-3*n^3*q^2*s+3*n^3*q*s^2-n^3*s^3+6*n^5+15*n ^4*q-15*n^4*s+12*n^3*q^2-24*n^3*q*s+12*n^3*s^2+3*n^2*q^3-9*n^2*q^2*s+9*n^2*q*s^ 2-3*n^2*s^3+15*n^4+30*n^3*q-30*n^3*s+18*n^2*q^2-36*n^2*q*s+18*n^2*s^2+3*n*q^3-9 *n*q^2*s+9*n*q*s^2-3*n*s^3+20*n^3+30*n^2*q-30*n^2*s+12*n*q^2-24*n*q*s+12*n*s^2+ q^3-3*q^2*s+3*q*s^2-s^3+15*n^2+15*n*q-15*n*s+3*q^2-6*q*s+3*s^2+6*n+3*q-3*s+1)*( 2*n+2*q-2*s-1)/(3*n^4*q^2+9*n^3*q^3-12*n^3*q^2*s+9*n^2*q^4-27*n^2*q^3*s+18*n^2* q^2*s^2+3*n*q^5-18*n*q^4*s+27*n*q^3*s^2-12*n*q^2*s^3-3*q^5*s+9*q^4*s^2-9*q^3*s^ 3+3*q^2*s^4-3*n^4*q-6*n^3*q^2+12*n^3*q*s+18*n^2*q^2*s-18*n^2*q*s^2+6*n*q^4-18*n *q^2*s^2+12*n*q*s^3+3*q^5-6*q^4*s+6*q^2*s^3-3*q*s^4+n^4-2*n^3*q-4*n^3*s-12*n^2* q^2+6*n^2*q*s+6*n^2*s^2-12*n*q^3+24*n*q^2*s-6*n*q*s^2-4*n*s^3-3*q^4+12*q^3*s-12 *q^2*s^2+2*q*s^3+s^4+2*n^3+6*n^2*q-6*n^2*s-12*n*q*s+6*n*s^2-3*q^3+6*q*s^2-2*s^3 +6*n*q+3*q^2-6*q*s-2*n+q+2*s-1)*diff(A[n](r,s),s)-(n^7+4*n^6*q-4*n^6*s+6*n^5*q^ 2-12*n^5*q*s+6*n^5*s^2+4*n^4*q^3-12*n^4*q^2*s+12*n^4*q*s^2-4*n^4*s^3+n^3*q^4-4* n^3*q^3*s+6*n^3*q^2*s^2-4*n^3*q*s^3+n^3*s^4+6*n^6+21*n^5*q-21*n^5*s+27*n^4*q^2-\ 54*n^4*q*s+27*n^4*s^2+15*n^3*q^3-45*n^3*q^2*s+45*n^3*q*s^2-15*n^3*s^3+3*n^2*q^4 -12*n^2*q^3*s+18*n^2*q^2*s^2-12*n^2*q*s^3+3*n^2*s^4+15*n^5+45*n^4*q-45*n^4*s+48 *n^3*q^2-96*n^3*q*s+48*n^3*s^2+21*n^2*q^3-63*n^2*q^2*s+63*n^2*q*s^2-21*n^2*s^3+ 3*n*q^4-12*n*q^3*s+18*n*q^2*s^2-12*n*q*s^3+3*n*s^4+20*n^4+50*n^3*q-50*n^3*s+42* n^2*q^2-84*n^2*q*s+42*n^2*s^2+13*n*q^3-39*n*q^2*s+39*n*q*s^2-13*n*s^3+q^4-4*q^3 *s+6*q^2*s^2-4*q*s^3+s^4+15*n^3+30*n^2*q-30*n^2*s+18*n*q^2-36*n*q*s+18*n*s^2+3* q^3-9*q^2*s+9*q*s^2-3*s^3+6*n^2+9*n*q-9*n*s+3*q^2-6*q*s+3*s^2+n+q-s)/(3*n^4*q^2 +9*n^3*q^3-12*n^3*q^2*s+9*n^2*q^4-27*n^2*q^3*s+18*n^2*q^2*s^2+3*n*q^5-18*n*q^4* s+27*n*q^3*s^2-12*n*q^2*s^3-3*q^5*s+9*q^4*s^2-9*q^3*s^3+3*q^2*s^4-3*n^4*q-6*n^3 *q^2+12*n^3*q*s+18*n^2*q^2*s-18*n^2*q*s^2+6*n*q^4-18*n*q^2*s^2+12*n*q*s^3+3*q^5 -6*q^4*s+6*q^2*s^3-3*q*s^4+n^4-2*n^3*q-4*n^3*s-12*n^2*q^2+6*n^2*q*s+6*n^2*s^2-\ 12*n*q^3+24*n*q^2*s-6*n*q*s^2-4*n*s^3-3*q^4+12*q^3*s-12*q^2*s^2+2*q*s^3+s^4+2*n ^3+6*n^2*q-6*n^2*s-12*n*q*s+6*n*s^2-3*q^3+6*q*s^2-2*s^3+6*n*q+3*q^2-6*q*s-2*n+q +2*s-1)*diff(diff(A[n](r,s),s),s)+(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2)*q^3/(3*n^2*q^ 2+6*n*q^3-6*n*q^2*s+3*q^4-6*q^3*s+3*q^2*s^2-3*n^2*q-3*n*q^2+6*n*q*s+3*q^2*s-3*q *s^2+n^2-3*n*q-2*n*s-3*q^2+3*q*s+s^2+2*n-2*s+1)/(n-s+1)*A[n+1](r,s)+diff(A[n+1] (r,s),s)+(3*n^4*q+9*n^3*q^2-12*n^3*q*s+9*n^2*q^3-27*n^2*q^2*s+18*n^2*q*s^2+3*n* q^4-18*n*q^3*s+27*n*q^2*s^2-12*n*q*s^3-3*q^4*s+9*q^3*s^2-9*q^2*s^3+3*q*s^4-3*n^ 4-3*n^3*q+12*n^3*s+6*n^2*q^2+9*n^2*q*s-18*n^2*s^2+9*n*q^3-12*n*q^2*s-9*n*q*s^2+ 12*n*s^3+3*q^4-9*q^3*s+6*q^2*s^2+3*q*s^3-3*s^4-8*n^3-17*n^2*q+24*n^2*s-9*n*q^2+ 34*n*q*s-24*n*s^2+9*q^2*s-17*q*s^2+8*s^3-6*n^2-13*n*q+12*n*s-6*q^2+13*q*s-6*s^2 -2*q+1)/(n+q-s-1)/(3*n^2*q^2+6*n*q^3-6*n*q^2*s+3*q^4-6*q^3*s+3*q^2*s^2-3*n^2*q-\ 3*n*q^2+6*n*q*s+3*q^2*s-3*q*s^2+n^2-3*n*q-2*n*s-3*q^2+3*q*s+s^2+2*n-2*s+1)*diff (diff(A[n+1](r,s),s),s)+(n^5+3*n^4*q-5*n^4*s+3*n^3*q^2-12*n^3*q*s+10*n^3*s^2+n^ 2*q^3-9*n^2*q^2*s+18*n^2*q*s^2-10*n^2*s^3-2*n*q^3*s+9*n*q^2*s^2-12*n*q*s^3+5*n* s^4+q^3*s^2-3*q^2*s^3+3*q*s^4-s^5+4*n^4+10*n^3*q-16*n^3*s+8*n^2*q^2-30*n^2*q*s+ 24*n^2*s^2+2*n*q^3-16*n*q^2*s+30*n*q*s^2-16*n*s^3-2*q^3*s+8*q^2*s^2-10*q*s^3+4* s^4+6*n^3+12*n^2*q-18*n^2*s+7*n*q^2-24*n*q*s+18*n*s^2+q^3-7*q^2*s+12*q*s^2-6*s^ 3+4*n^2+6*n*q-8*n*s+2*q^2-6*q*s+4*s^2+n+q-s)/(n+q-s-1)/(3*n^2*q^2+6*n*q^3-6*n*q ^2*s+3*q^4-6*q^3*s+3*q^2*s^2-3*n^2*q-3*n*q^2+6*n*q*s+3*q^2*s-3*q*s^2+n^2-3*n*q-\ 2*n*s-3*q^2+3*q*s+s^2+2*n-2*s+1)*diff(diff(diff(A[n+1](r,s),s),s),s) = 0 ------------------------------------------------- This took, 0.250, seconds. -------------------------------------------- Theorem: define the Abel-sum type sequence by n ----- \ 4 (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)^4*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s 4 3 3 2 2 2 3 2 3 3 (p - 3 p r + p s + 3 p r - 3 p r s - p r + 3 p r s - r s - 10 p 2 2 2 3 2 2 + 21 p r - 9 p s - 12 p r + 18 p r s + r - 9 r s + 35 p - 44 p r 2 / + 26 p s + 9 r - 26 r s - 50 p + 26 r - 24 s + 24) A[n](r, s) / ( / 2 2 6 5 5 (p r + p s - r - r s - r - s) (p - r - 1) ) - (3 p - 14 p r + 4 p s 4 2 4 3 3 3 2 2 4 2 3 + 25 p r - 20 p r s - 20 p r + 40 p r s + 5 p r - 40 p r s 5 4 6 5 5 4 4 + 2 p r + 20 p r s - r - 4 r s - 39 p + 149 p r - 46 p s 3 2 3 2 3 2 2 4 3 - 206 p r + 184 p r s + 114 p r - 276 p r s - 11 p r + 184 p r s 5 4 4 3 3 2 2 2 - 7 r - 46 r s + 202 p - 606 p r + 202 p s + 606 p r - 606 p r s 3 2 3 3 2 2 - 202 p r + 606 p r s - 202 r s - 535 p + 1178 p r - 427 p s 2 3 2 2 - 751 p r + 854 p r s + 108 r - 427 r s + 767 p - 1093 p r + 441 p s 2 /d \ / + 326 r - 441 r s - 566 p + 386 r - 180 s + 168) |-- A[n](r, s)| / ( \dr / / 2 2 2 2 2 (p - r - 1) (p - 2 p r + r - 3 p + 3 r + 2) (p r + p s - 2 p r 3 2 2 6 - 2 p r s + r + r s - 3 p r - 3 p s + 3 r + 3 r s + 2 r + 2 s)) + (3 p 5 5 4 2 4 3 2 2 4 - 12 p r + 6 p s + 15 p r - 30 p r s + 60 p r s - 15 p r 2 3 5 4 6 5 5 4 - 60 p r s + 12 p r + 30 p r s - 3 r - 6 r s - 42 p + 138 p r 4 3 2 3 2 3 2 2 4 - 72 p s - 132 p r + 288 p r s - 12 p r - 432 p r s + 78 p r 3 5 4 4 3 3 2 2 + 288 p r s - 30 r - 72 r s + 236 p - 611 p r + 333 p s + 417 p r 2 3 2 4 3 3 - 999 p r s + 55 p r + 999 p r s - 97 r - 333 r s - 680 p 2 2 2 3 2 + 1296 p r - 744 p s - 552 p r + 1488 p r s - 64 r - 744 r s 2 2 + 1057 p - 1309 p r + 805 p s + 252 r - 805 r s - 838 p + 498 r - 340 s / 2 \ |d | / 3 3 2 2 2 3 + 264) |--- A[n](r, s)| / ((p r + p s - 3 p r - 3 p r s + 3 p r | 2 | / \dr / 2 4 3 2 2 2 3 + 3 p r s - r - r s - 6 p r - 6 p s + 12 p r + 12 p r s - 6 r 2 2 - 6 r s + 11 p r + 11 p s - 11 r - 11 r s - 6 r - 6 s) 2 2 4 3 2 2 2 (p - 2 p r + r - 3 p + 3 r + 2)) - (p + 4 p s - 6 p r - 12 p r s 3 2 4 3 3 2 2 + 8 p r + 12 p r s - 3 r - 4 r s - 10 p - 30 p s + 30 p r 3 2 2 2 + 60 p r s - 20 r - 30 r s + 35 p + 70 p s - 35 r - 70 r s - 50 p / 3 \ |d | / 3 3 2 2 2 - 50 s + 24) |--- A[n](r, s)| / (p r + p s - 3 p r - 3 p r s | 3 | / \dr / 3 2 4 3 2 2 2 + 3 p r + 3 p r s - r - r s - 6 p r - 6 p s + 12 p r + 12 p r s 3 2 2 - 6 r - 6 r s + 11 p r + 11 p s - 11 r - 11 r s - 6 r - 6 s) / 4 \ |d | 4 3 4 2 4 2 4 3 3 4 + |--- A[n](r, s)| - (n p - 3 n p r + 3 n p r - n r + 4 n p | 4 | \dr / 3 3 3 2 2 3 3 2 5 2 4 - 12 n p r + 12 n p r - 4 n p r + 6 n p - 18 n p r 2 3 2 2 2 3 6 5 4 2 3 3 + 18 n p r - 6 n p r + 4 n p - 12 n p r + 12 n p r - 4 n p r 7 6 5 2 4 3 4 2 4 4 2 3 3 + p - 3 p r + 3 p r - p r - 9 n p + 18 n p r - 9 n r - 36 n p 3 2 3 2 2 4 2 3 2 2 2 5 + 72 n p r - 36 n p r - 54 n p + 108 n p r - 54 n p r - 36 n p 4 3 2 6 5 4 2 4 4 + 72 n p r - 36 n p r - 9 p + 18 p r - 9 p r + 26 n p - 26 n r 3 2 3 2 3 2 2 4 3 + 104 n p - 104 n p r + 156 n p - 156 n p r + 104 n p - 104 n p r 5 4 4 3 2 2 3 4 + 26 p - 26 p r - 24 n - 96 n p - 144 n p - 96 n p - 24 p ) / 4 3 2 3 A[n + 1](r, s) / ((n + 4 n + 6 n + 4 n + 1) (p - r - 1) (r + s)) + ( / 4 5 4 4 4 3 2 4 2 3 4 4 4 5 4 n p - 20 n p r + 40 n p r - 40 n p r + 20 n p r - 4 n r 3 6 3 5 3 4 2 3 3 3 3 2 4 + 12 n p - 56 n p r + 100 n p r - 80 n p r + 20 n p r 3 5 3 6 2 7 2 6 2 5 2 2 3 4 + 8 n p r - 4 n r + 12 n p - 48 n p r + 60 n p r - 60 n p r 2 2 5 2 6 8 7 6 2 5 3 + 48 n p r - 12 n p r + 4 n p - 8 n p r - 20 n p r + 80 n p r 4 4 3 5 2 6 8 7 2 6 3 - 100 n p r + 56 n p r - 12 n p r + 4 p r - 20 p r + 40 p r 5 4 4 5 3 6 4 4 4 3 4 2 2 - 40 p r + 20 p r - 4 p r - 46 n p + 184 n p r - 276 n p r 4 3 4 4 3 5 3 4 3 3 2 + 184 n p r - 46 n r - 140 n p + 516 n p r - 664 n p r 3 2 3 3 4 3 5 2 6 2 5 + 296 n p r + 36 n p r - 44 n r - 138 n p + 408 n p r 2 4 2 2 3 3 2 2 4 2 5 2 6 - 246 n p r - 336 n p r + 474 n p r - 168 n p r + 6 n r 7 6 5 2 4 3 3 4 - 40 n p + 4 n p r + 396 n p r - 824 n p r + 656 n p r 2 5 6 8 7 6 2 5 3 - 204 n p r + 12 n p r + 4 p - 72 p r + 254 p r - 376 p r 4 4 3 5 2 6 4 3 4 2 4 2 + 264 p r - 80 p r + 6 p r + 202 n p - 606 n p r + 606 n p r 4 3 3 4 3 3 3 2 2 3 3 - 202 n r + 624 n p - 1688 n p r + 1320 n p r - 72 n p r 3 4 2 5 2 4 2 3 2 2 2 3 - 184 n r + 594 n p - 1098 n p r - 336 n p r + 1656 n p r 2 4 2 5 6 5 4 2 - 882 n p r + 66 n r + 120 n p + 468 n p r - 2268 n p r 3 3 2 4 5 6 7 6 + 2800 n p r - 1272 n p r + 156 n p r - 4 n r - 52 p + 484 p r 5 2 4 3 3 4 2 5 6 4 2 - 1218 p r + 1274 p r - 574 p r + 90 p r - 4 p r - 427 n p 4 4 2 3 3 3 2 3 2 + 854 n p r - 427 n r - 1332 n p + 2288 n p r - 580 n p r 3 3 2 4 2 3 2 2 2 2 3 - 376 n r - 1158 n p + 636 n p r + 2478 n p r - 2232 n p r 2 4 5 4 3 2 2 3 + 276 n r + 16 n p - 2396 n p r + 5428 n p r - 3776 n p r 4 5 6 5 4 2 3 3 + 772 n p r - 44 n r + 270 p - 1604 p r + 2812 p r - 1940 p r 2 4 5 6 4 4 3 2 3 + 511 p r - 50 p r + r + 441 n p - 441 n r + 1360 n p - 956 n p r 3 2 2 3 2 2 2 2 2 3 - 404 n r + 870 n p + 1470 n p r - 2904 n p r + 564 n r 4 3 2 2 3 4 5 - 760 n p + 4780 n p r - 5700 n p r + 1864 n p r - 184 n r - 722 p 4 3 2 2 3 4 5 4 + 2850 p r - 3310 p r + 1410 p r - 239 p r + 11 r - 180 n 3 3 2 2 2 2 2 3 - 500 n p - 220 n r + 186 n p - 1872 n p r + 606 n r + 1528 n p 2 2 3 4 3 2 2 - 4212 n p r + 2340 n p r - 376 n r + 1068 p - 2744 p r + 2010 p r 3 4 3 2 2 2 - 560 p r + 46 r - 48 n - 474 n p + 330 n r - 1208 n p + 1468 n p r 2 3 2 2 3 2 - 404 n r - 876 p + 1420 p r - 686 p r + 94 r + 72 n + 364 n p 2 2 - 220 n r + 393 p - 422 p r + 101 r - 48 n - 103 p + 55 r + 12) /d \ / 3 2 |-- A[n + 1](r, s)| / ((n p - n r - n + p - r - 1) (n + 3 n + 3 n + 1) \dr / / 2 2 2 4 5 4 4 (p - 2 p r + r - 3 p + 3 r + 2) (r + s)) - (6 n p - 30 n p r 4 3 2 4 2 3 4 4 4 5 3 6 3 5 + 60 n p r - 60 n p r + 30 n p r - 6 n r + 12 n p - 48 n p r 3 4 2 3 2 4 3 5 3 6 2 7 2 6 + 60 n p r - 60 n p r + 48 n p r - 12 n r + 6 n p - 6 n p r 2 5 2 2 4 3 2 3 4 2 2 5 2 6 - 54 n p r + 150 n p r - 150 n p r + 54 n p r + 6 n p r 2 7 7 6 2 5 3 3 5 2 6 - 6 n r + 12 n p r - 48 n p r + 60 n p r - 60 n p r + 48 n p r 7 7 2 6 3 5 4 4 5 3 6 - 12 n p r + 6 p r - 30 p r + 60 p r - 60 p r + 30 p r 2 7 4 4 4 3 4 2 2 4 3 4 4 - 6 p r - 72 n p + 288 n p r - 432 n p r + 288 n p r - 72 n r 3 5 3 4 3 3 2 3 2 3 3 4 - 144 n p + 432 n p r - 288 n p r - 288 n p r + 432 n p r 3 5 2 6 2 5 2 4 2 2 3 3 - 144 n r - 60 n p - 72 n p r + 828 n p r - 1392 n p r 2 2 4 2 5 2 6 7 6 + 828 n p r - 72 n p r - 60 n r + 12 n p - 204 n p r 5 2 4 3 3 4 2 5 6 + 540 n p r - 348 n p r - 348 n p r + 540 n p r - 204 n p r 7 7 6 2 5 3 4 4 3 5 + 12 n r + 12 p r - 144 p r + 468 p r - 672 p r + 468 p r 2 6 7 4 3 4 2 4 2 4 3 - 144 p r + 12 p r + 333 n p - 999 n p r + 999 n p r - 333 n r 3 4 3 3 3 2 2 3 3 3 4 + 656 n p - 1292 n p r - 60 n p r + 1372 n p r - 676 n r 2 5 2 4 2 3 2 2 2 3 2 4 + 168 n p + 1128 n p r - 4194 n p r + 4134 n p r - 1038 n p r 2 5 6 5 4 2 3 3 - 198 n r - 156 n p + 1272 n p r - 2052 n p r - 60 n p r 2 4 5 6 7 6 5 2 + 2112 n p r - 1260 n p r + 144 n r + 6 p - 198 p r + 1230 p r 4 3 3 4 2 5 6 7 4 2 - 2734 p r + 2719 p r - 1209 p r + 193 p r - 7 r - 744 n p 4 4 2 3 3 3 2 3 2 + 1488 n p r - 744 n r - 1388 n p + 1188 n p r + 1788 n p r 3 3 2 4 2 3 2 2 2 2 3 - 1588 n r + 144 n p - 4740 n p r + 8892 n p r - 4140 n p r 2 4 5 4 3 2 2 3 - 156 n r + 792 n p - 3672 n p r + 2604 n p r + 3324 n p r 4 5 6 5 4 2 3 3 - 3732 n p r + 684 n r - 84 p + 1296 p r - 5076 p r + 7636 p r 2 4 5 6 4 4 3 2 - 4896 p r + 1212 p r - 88 r + 805 n p - 805 n r + 1252 n p 3 3 2 2 3 2 2 2 2 + 716 n p r - 1968 n r - 1548 n p + 8400 n p r - 7326 n p r 2 3 4 3 2 2 3 + 474 n r - 1968 n p + 4776 n p r + 1236 n p r - 5708 n p r 4 5 4 3 2 2 3 4 + 1664 n r + 474 p - 4338 p r + 11064 p r - 10652 p r + 3899 p r 5 4 3 3 2 2 2 - 447 r - 340 n - 132 n p - 1228 n r + 2796 n p - 5988 n p r 2 2 3 2 2 3 4 + 1152 n r + 2400 n p - 1608 n p r - 4380 n p r + 2228 n r - 1384 p 3 2 2 3 4 3 2 + 7936 p r - 12708 p r + 7012 p r - 1196 r - 304 n - 1842 n p 2 2 2 3 2 + 930 n r - 1140 n p - 1404 n p r + 1632 n r + 2227 p - 7821 p r 2 3 2 2 + 7119 p r - 1829 r + 264 n - 68 n p + 596 n r - 1940 p + 3812 p r / 2 \ 2 |d | / 2 2 - 1608 r + 80 n + 837 p - 757 r - 148) |--- A[n + 1](r, s)| / ((n p | 2 | / \dr / 2 2 2 2 2 2 2 2 - 2 n p r + n r - 3 n p + 3 n r + 2 n p - 4 n p r + 2 n r + 2 n 2 2 2 - 6 n p + 6 n r + p - 2 p r + r + 4 n - 3 p + 3 r + 2) (n + 2 n + 1) (r + s) 3 2 2 3 2 2 (p - 3 p r + 3 p r - r - 6 p + 12 p r - 6 r + 11 p - 11 r - 6)) + 2 ( 4 3 4 2 4 2 4 3 3 4 3 2 2 2 n p - 6 n p r + 6 n p r - 2 n r + 2 n p - 12 n p r 3 3 3 4 2 4 2 3 2 2 4 2 5 + 16 n p r - 6 n r + 6 n p r - 12 n p r + 12 n p r - 6 n r 4 2 3 3 2 4 6 4 3 3 4 + 6 n p r - 16 n p r + 12 n p r - 2 n r + 2 p r - 6 p r 2 5 6 4 2 4 4 2 3 3 + 6 p r - 2 p r - 15 n p + 30 n p r - 15 n r - 12 n p 3 2 3 2 3 3 2 4 2 3 2 2 2 - 24 n p r + 84 n p r - 48 n r + 6 n p - 60 n p r + 54 n p r 2 3 2 4 4 3 2 2 3 4 + 48 n p r - 48 n r + 12 n p r - 84 n p r + 120 n p r - 36 n p r 5 4 2 3 3 2 4 5 6 4 - 12 n r + 6 p r - 36 p r + 57 p r - 30 p r + 3 r + 35 n p 4 3 2 3 3 2 2 3 2 2 - 35 n r + 10 n p + 120 n p r - 130 n r - 48 n p + 174 n p r 2 2 2 3 4 3 2 2 3 + 6 n p r - 132 n r + 6 n p - 120 n p r + 354 n p r - 232 n p r 4 4 3 2 2 3 4 5 4 - 8 n r + 6 p r - 72 p r + 190 p r - 153 p r + 29 r - 25 n 3 3 2 2 2 2 2 3 + 40 n p - 140 n r + 120 n p - 120 n p r - 150 n r - 52 n p 2 2 3 4 3 2 2 + 396 n p r - 516 n p r + 72 n r + 2 p - 60 p r + 288 p r 3 4 3 2 2 2 - 364 p r + 109 r - 52 n - 90 n p - 66 n r + 150 n p - 480 n p r 2 3 2 2 3 2 + 174 n r - 18 p + 204 p r - 444 p r + 206 r - 6 n - 160 n p 2 2 + 148 n r + 55 p - 270 p r + 209 r + 44 n - 65 p + 109 r + 23) / 3 \ |d | / 4 3 4 2 4 2 4 3 4 2 |--- A[n + 1](r, s)| / ((n p - 3 n p r + 3 n p r - n r - 6 n p | 3 | / \dr / 4 4 2 3 3 3 2 3 2 3 3 + 12 n p r - 6 n r + 4 n p - 12 n p r + 12 n p r - 4 n r 4 4 3 2 3 3 2 2 3 + 11 n p - 11 n r - 24 n p + 48 n p r - 24 n r + 6 n p 2 2 2 2 2 3 4 3 3 2 2 - 18 n p r + 18 n p r - 6 n r - 6 n + 44 n p - 44 n r - 36 n p 2 2 2 3 2 2 3 3 + 72 n p r - 36 n r + 4 n p - 12 n p r + 12 n p r - 4 n r - 24 n 2 2 2 2 3 2 2 + 66 n p - 66 n r - 24 n p + 48 n p r - 24 n r + p - 3 p r + 3 p r 3 2 2 2 - r - 36 n + 44 n p - 44 n r - 6 p + 12 p r - 6 r - 24 n + 11 p - 11 r 4 3 2 2 3 4 3 2 - 6) (r + s)) - (n + 4 n r + 6 n r + 4 n r + r + 4 n + 12 n r 2 3 2 2 + 12 n r + 4 r + 6 n + 12 n r + 6 r + 4 n + 4 r + 1) / 4 \ |d | / 4 3 2 |--- A[n + 1](r, s)| / ((n + 4 n + 6 n + 4 n + 1) (r + s)) = 0 | 4 | / \dr / 2 2 2 (n + 2 n q - 2 n s + q - 2 q s + s - 3 n - 3 q + 3 s + 2) A[n](r, s) - ----------------------------------------------------------------------- + ( 2 (n + q - s) 3 2 2 2 2 3 2 3 n + 9 n q - 9 n s + 9 n q - 18 n q s + 9 n s + 3 q - 9 q s 2 3 2 2 2 + 9 q s - 3 s - 9 n - 18 n q + 18 n s - 9 q + 18 q s - 9 s + 7 n /d \ + 7 q - 7 s - 2) |-- A[n](r, s)|/(%1 (n + q - s)) - \ds / 2 2 2 (3 n + 6 n q - 6 n s + 3 q - 6 q s + 3 s - 6 n - 6 q + 6 s + 2) / 2 \ / 3 \ |d | |d | 3 2 2 2 |--- A[n](r, s)|/(%1) + |--- A[n](r, s)| - (n + 3 n q - 3 n s + 3 n q | 2 | | 3 | \ds / \ds / 2 3 2 2 3 2 - 6 n q s + 3 n s + q - 3 q s + 3 q s - s - 3 n - 6 n q + 6 n s 2 2 4 / - 3 q + 6 q s - 3 s + 2 n + 2 q - 2 s) q A[n + 1](r, s) / ( / 4 3 2 4 6 3 5 4 (n + 4 n + 6 n + 4 n + 1) (q + n - s + 1) ) - (4 n q + 20 n q 5 3 4 5 4 4 4 3 2 3 6 - 24 n q s + 40 n q - 100 n q s + 60 n q s + 40 n q 3 5 3 4 2 3 3 3 2 7 2 6 - 160 n q s + 200 n q s - 80 n q s + 20 n q - 120 n q s 2 5 2 2 4 3 2 3 4 8 7 + 240 n q s - 200 n q s + 60 n q s + 4 n q - 40 n q s 6 2 5 3 4 4 3 5 8 7 2 + 120 n q s - 160 n q s + 100 n q s - 24 n q s - 4 q s + 20 q s 6 3 5 4 4 5 3 6 6 2 5 3 - 40 q s + 40 q s - 20 q s + 4 q s - 6 n q - 32 n q 5 2 4 4 4 3 4 2 2 3 5 + 36 n q s - 64 n q + 160 n q s - 90 n q s - 56 n q 3 4 3 3 2 3 2 3 2 6 2 5 + 256 n q s - 320 n q s + 120 n q s - 14 n q + 168 n q s 2 4 2 2 3 3 2 2 4 7 6 - 384 n q s + 320 n q s - 90 n q s + 8 n q + 28 n q s 5 2 4 3 3 4 2 5 8 7 - 168 n q s + 256 n q s - 160 n q s + 36 n q s + 4 q - 8 q s 6 2 5 3 4 4 3 5 2 6 6 5 2 - 14 q s + 56 q s - 64 q s + 32 q s - 6 q s + 4 n q + 18 n q 5 4 3 4 2 4 2 3 4 3 3 - 24 n q s + 14 n q - 90 n q s + 60 n q s - 38 n q - 56 n q s 3 2 2 3 3 2 5 2 4 2 3 2 + 180 n q s - 80 n q s - 78 n q + 114 n q s + 84 n q s 2 2 3 2 4 6 5 4 2 - 180 n q s + 60 n q s - 52 n q + 156 n q s - 114 n q s 3 3 2 4 5 7 6 5 2 - 56 n q s + 90 n q s - 24 n q s - 12 q + 52 q s - 78 q s 4 3 3 4 2 5 6 6 5 5 + 38 q s + 14 q s - 18 q s + 4 q s - n - 2 n q + 6 n s 4 2 4 4 2 3 3 3 2 3 2 + 29 n q + 10 n q s - 15 n s + 92 n q - 116 n q s - 20 n q s 3 3 2 4 2 3 2 2 2 2 3 2 4 + 20 n s + 96 n q - 276 n q s + 174 n q s + 20 n q s - 15 n s 5 4 3 2 2 3 4 5 + 36 n q - 192 n q s + 276 n q s - 116 n q s - 10 n q s + 6 n s 6 5 4 2 3 3 2 4 5 6 5 + 2 q - 36 q s + 96 q s - 92 q s + 29 q s + 2 q s - s - n 4 4 3 2 3 3 2 2 3 - 21 n q + 5 n s - 38 n q + 84 n q s - 10 n s + 6 n q 2 2 2 2 2 3 4 3 2 2 + 114 n q s - 126 n q s + 10 n s + 42 n q - 12 n q s - 114 n q s 3 4 5 4 3 2 2 3 4 5 + 84 n q s - 5 n s + 18 q - 42 q s + 6 q s + 38 q s - 21 q s + s 4 3 3 2 2 2 2 2 3 + 4 n - 8 n q - 16 n s - 54 n q + 24 n q s + 24 n s - 48 n q 2 2 3 4 3 2 2 3 + 108 n q s - 24 n q s - 16 n s - 8 q + 48 q s - 54 q s + 8 q s 4 3 2 2 2 2 3 + 4 s + 6 n + 22 n q - 18 n s - 4 n q - 44 n q s + 18 n s - 12 q 2 2 3 2 2 2 + 4 q s + 22 q s - 6 s - n + 18 n q + 2 n s + 7 q - 18 q s - s - 5 n /d \ / 2 5 4 + 3 q + 5 s - 2) |-- A[n + 1](r, s)| / ((q + n - s + 1) (n + n q \ds / / 4 4 3 3 3 2 2 2 - n s + 5 n + 4 n q - 4 n s + 10 n + 6 n q - 6 n s + 10 n + 4 n q - 4 n s + 5 n + q - s + 1) 2 2 2 7 2 (n + 2 n q - 2 n s + q - 2 q s + s + n + q - s) (n + q - s)) - (6 n q 6 3 6 2 5 4 5 3 5 2 2 4 5 + 30 n q - 42 n q s + 60 n q - 180 n q s + 126 n q s + 60 n q 4 4 4 3 2 4 2 3 3 6 3 5 - 300 n q s + 450 n q s - 210 n q s + 30 n q - 240 n q s 3 4 2 3 3 3 3 2 4 2 7 2 6 + 600 n q s - 600 n q s + 210 n q s + 6 n q - 90 n q s 2 5 2 2 4 3 2 3 4 2 2 5 7 + 360 n q s - 600 n q s + 450 n q s - 126 n q s - 12 n q s 6 2 5 3 4 4 3 5 2 6 + 90 n q s - 240 n q s + 300 n q s - 180 n q s + 42 n q s 7 2 6 3 5 4 4 5 3 6 2 7 7 + 6 q s - 30 q s + 60 q s - 60 q s + 30 q s - 6 q s - 12 n q 6 2 6 5 3 5 2 5 2 4 4 - 60 n q + 84 n q s - 108 n q + 360 n q s - 252 n q s - 72 n q 4 3 4 2 2 4 3 3 5 3 4 + 540 n q s - 900 n q s + 420 n q s + 12 n q + 288 n q s 3 3 2 3 2 3 3 4 2 6 2 5 - 1080 n q s + 1200 n q s - 420 n q s + 36 n q - 36 n q s 2 4 2 2 3 3 2 2 4 2 5 7 - 432 n q s + 1080 n q s - 900 n q s + 252 n q s + 12 n q 6 5 2 4 3 3 4 2 5 - 72 n q s + 36 n q s + 288 n q s - 540 n q s + 360 n q s 6 7 6 2 5 3 4 4 3 5 - 84 n q s - 12 q s + 36 q s - 12 q s - 72 q s + 108 q s 2 6 7 7 6 6 5 2 5 - 60 q s + 12 q s + 7 n + 25 n q - 49 n s - 15 n q - 150 n q s 5 2 4 3 4 2 4 2 4 3 3 4 + 147 n s - 161 n q + 75 n q s + 375 n q s - 245 n s - 242 n q 3 3 3 2 2 3 3 3 4 2 5 + 644 n q s - 150 n q s - 500 n q s + 245 n s - 138 n q 2 4 2 3 2 2 2 3 2 4 2 5 + 726 n q s - 966 n q s + 150 n q s + 375 n q s - 147 n s 6 5 4 2 3 3 2 4 - 18 n q + 276 n q s - 726 n q s + 644 n q s - 75 n q s 5 6 7 6 5 2 4 3 - 150 n q s + 49 n s + 6 q + 18 q s - 138 q s + 242 q s 3 4 2 5 6 7 6 5 5 - 161 q s + 15 q s + 25 q s - 7 s + 10 n + 96 n q - 60 n s 4 2 4 4 2 3 3 3 2 + 234 n q - 480 n q s + 150 n s + 196 n q - 936 n q s 3 2 3 3 2 3 2 2 2 2 3 + 960 n q s - 200 n s - 588 n q s + 1404 n q s - 960 n q s 2 4 5 3 2 2 3 4 5 + 150 n s - 72 n q + 588 n q s - 936 n q s + 480 n q s - 60 n s 6 5 3 3 2 4 5 6 5 4 - 24 q + 72 q s - 196 q s + 234 q s - 96 q s + 10 s - 21 n - n q 4 3 2 3 3 2 2 3 2 2 + 105 n s + 164 n q + 4 n q s - 210 n s + 264 n q - 492 n q s 2 2 2 3 4 3 2 2 3 - 6 n q s + 210 n s + 138 n q - 528 n q s + 492 n q s + 4 n q s 4 5 4 3 2 2 3 4 5 - 105 n s + 18 q - 138 q s + 264 q s - 164 q s - q s + 21 s 4 3 3 2 2 2 2 2 - 46 n - 140 n q + 184 n s - 108 n q + 420 n q s - 276 n s 3 2 2 3 4 3 + 16 n q + 216 n q s - 420 n q s + 184 n s + 28 q - 16 q s 2 2 3 4 3 2 2 2 - 108 q s + 140 q s - 46 s - 19 n - 81 n q + 57 n s - 99 n q 2 3 2 2 3 2 + 162 n q s - 57 n s - 29 q + 99 q s - 81 q s + 19 s + 6 n + 8 n q / 2 \ 2 2 |d | - 12 n s - 10 q - 8 q s + 6 s + n + 9 q - s - 2) |--- A[n + 1](r, s)| | 2 | \ds / / 6 5 5 4 2 4 4 2 5 4 / ((n + 2 n q - 2 n s + n q - 2 n q s + n s + 5 n + 9 n q / 4 3 2 3 3 2 4 3 3 - 9 n s + 4 n q - 8 n q s + 4 n s + 10 n + 16 n q - 16 n s 2 2 2 2 2 3 2 2 2 + 6 n q - 12 n q s + 6 n s + 10 n + 14 n q - 14 n s + 4 n q 2 2 2 2 - 8 n q s + 4 n s + 5 n + 6 n q - 6 n s + q - 2 q s + s + n + q - s) 2 6 5 2 5 4 3 (q + n - s + 1) %1) - 2 (2 n q + 6 n q - 12 n q s + 6 n q 4 2 4 2 3 4 3 3 3 2 2 - 30 n q s + 30 n q s + 2 n q - 24 n q s + 60 n q s 3 3 2 4 2 3 2 2 2 3 2 4 - 40 n q s - 6 n q s + 36 n q s - 60 n q s + 30 n q s 4 2 3 3 2 4 5 4 3 3 4 + 6 n q s - 24 n q s + 30 n q s - 12 n q s - 2 q s + 6 q s 2 5 6 6 5 5 4 2 4 - 6 q s + 2 q s - 3 n - 6 n q + 18 n s + 3 n q + 30 n q s 4 2 3 3 3 2 3 2 3 3 2 4 - 45 n s + 12 n q - 12 n q s - 60 n q s + 60 n s + 6 n q 2 3 2 2 2 2 3 2 4 4 - 36 n q s + 18 n q s + 60 n q s - 45 n s - 12 n q s 3 2 2 3 4 5 4 2 3 3 + 36 n q s - 12 n q s - 30 n q s + 18 n s + 6 q s - 12 q s 2 4 5 6 5 4 4 3 2 + 3 q s + 6 q s - 3 s - 7 n - 27 n q + 35 n s - 26 n q 3 3 2 2 2 2 2 2 3 4 + 108 n q s - 70 n s + 78 n q s - 162 n q s + 70 n s + 6 n q 2 2 3 4 4 2 3 4 5 - 78 n q s + 108 n q s - 35 n s - 6 q s + 26 q s - 27 q s + 7 s 4 3 3 2 2 2 2 2 3 + n - 20 n q - 4 n s - 36 n q + 60 n q s + 6 n s - 12 n q 2 2 3 4 3 2 2 3 + 72 n q s - 60 n q s - 4 n s + 2 q + 12 q s - 36 q s + 20 q s 4 3 2 2 2 2 3 + s + 14 n + 12 n q - 42 n s - 12 n q - 24 n q s + 42 n s - 6 q 2 2 3 2 2 + 12 q s + 12 q s - 14 s + 11 n + 18 n q - 22 n s + q - 18 q s / 3 \ 2 |d | / 7 6 6 + 11 s + n + 5 q - s - 1) |--- A[n + 1](r, s)| / ((n + 3 n q - 3 n s | 3 | / \ds / 5 2 5 5 2 4 3 4 2 4 2 4 3 + 3 n q - 6 n q s + 3 n s + n q - 3 n q s + 3 n q s - n s 6 5 5 4 2 4 4 2 3 3 + 4 n + 12 n q - 12 n s + 12 n q - 24 n q s + 12 n s + 4 n q 3 2 3 2 3 3 5 4 4 3 2 - 12 n q s + 12 n q s - 4 n s + 5 n + 17 n q - 17 n s + 18 n q 3 3 2 2 3 2 2 2 2 2 3 - 36 n q s + 18 n s + 6 n q - 18 n q s + 18 n q s - 6 n s 3 3 2 2 2 2 2 3 2 + 8 n q - 8 n s + 12 n q - 24 n q s + 12 n s + 4 n q - 12 n q s 2 3 3 2 2 2 2 + 12 n q s - 4 n s - 5 n - 3 n q + 3 n s + 3 n q - 6 n q s + 3 n s 3 2 2 3 2 + q - 3 q s + 3 q s - s - 4 n - 4 n q + 4 n s - n - q + s) 4 3 2 2 3 4 3 2 (q + n - s + 1)) - (n - 4 n s + 6 n s - 4 n s + s + 4 n - 12 n s 2 3 2 2 + 12 n s - 4 s + 6 n - 12 n s + 6 s + 4 n - 4 s + 1) / 4 \ |d | / 5 4 4 4 3 3 3 |--- A[n + 1](r, s)| / (n + n q - n s + 5 n + 4 n q - 4 n s + 10 n | 4 | / \ds / 2 2 2 + 6 n q - 6 n s + 10 n + 4 n q - 4 n s + 5 n + q - s + 1) = 0 2 2 2 %1 := n + 2 n q - 2 n s + q - 2 q s + s - n - q + s and in Maple notation (p^4-3*p^3*r+p^3*s+3*p^2*r^2-3*p^2*r*s-p*r^3+3*p*r^2*s-r^3*s-10*p^3+21*p^2*r-9* p^2*s-12*p*r^2+18*p*r*s+r^3-9*r^2*s+35*p^2-44*p*r+26*p*s+9*r^2-26*r*s-50*p+26*r -24*s+24)/(p*r+p*s-r^2-r*s-r-s)/(p-r-1)^2*A[n](r,s)-(3*p^6-14*p^5*r+4*p^5*s+25* p^4*r^2-20*p^4*r*s-20*p^3*r^3+40*p^3*r^2*s+5*p^2*r^4-40*p^2*r^3*s+2*p*r^5+20*p* r^4*s-r^6-4*r^5*s-39*p^5+149*p^4*r-46*p^4*s-206*p^3*r^2+184*p^3*r*s+114*p^2*r^3 -276*p^2*r^2*s-11*p*r^4+184*p*r^3*s-7*r^5-46*r^4*s+202*p^4-606*p^3*r+202*p^3*s+ 606*p^2*r^2-606*p^2*r*s-202*p*r^3+606*p*r^2*s-202*r^3*s-535*p^3+1178*p^2*r-427* p^2*s-751*p*r^2+854*p*r*s+108*r^3-427*r^2*s+767*p^2-1093*p*r+441*p*s+326*r^2-\ 441*r*s-566*p+386*r-180*s+168)/(p-r-1)/(p^2-2*p*r+r^2-3*p+3*r+2)/(p^2*r+p^2*s-2 *p*r^2-2*p*r*s+r^3+r^2*s-3*p*r-3*p*s+3*r^2+3*r*s+2*r+2*s)*diff(A[n](r,s),r)+(3* p^6-12*p^5*r+6*p^5*s+15*p^4*r^2-30*p^4*r*s+60*p^3*r^2*s-15*p^2*r^4-60*p^2*r^3*s +12*p*r^5+30*p*r^4*s-3*r^6-6*r^5*s-42*p^5+138*p^4*r-72*p^4*s-132*p^3*r^2+288*p^ 3*r*s-12*p^2*r^3-432*p^2*r^2*s+78*p*r^4+288*p*r^3*s-30*r^5-72*r^4*s+236*p^4-611 *p^3*r+333*p^3*s+417*p^2*r^2-999*p^2*r*s+55*p*r^3+999*p*r^2*s-97*r^4-333*r^3*s-\ 680*p^3+1296*p^2*r-744*p^2*s-552*p*r^2+1488*p*r*s-64*r^3-744*r^2*s+1057*p^2-\ 1309*p*r+805*p*s+252*r^2-805*r*s-838*p+498*r-340*s+264)/(p^3*r+p^3*s-3*p^2*r^2-\ 3*p^2*r*s+3*p*r^3+3*p*r^2*s-r^4-r^3*s-6*p^2*r-6*p^2*s+12*p*r^2+12*p*r*s-6*r^3-6 *r^2*s+11*p*r+11*p*s-11*r^2-11*r*s-6*r-6*s)/(p^2-2*p*r+r^2-3*p+3*r+2)*diff(diff (A[n](r,s),r),r)-(p^4+4*p^3*s-6*p^2*r^2-12*p^2*r*s+8*p*r^3+12*p*r^2*s-3*r^4-4*r ^3*s-10*p^3-30*p^2*s+30*p*r^2+60*p*r*s-20*r^3-30*r^2*s+35*p^2+70*p*s-35*r^2-70* r*s-50*p-50*s+24)/(p^3*r+p^3*s-3*p^2*r^2-3*p^2*r*s+3*p*r^3+3*p*r^2*s-r^4-r^3*s-\ 6*p^2*r-6*p^2*s+12*p*r^2+12*p*r*s-6*r^3-6*r^2*s+11*p*r+11*p*s-11*r^2-11*r*s-6*r -6*s)*diff(diff(diff(A[n](r,s),r),r),r)+diff(diff(diff(diff(A[n](r,s),r),r),r), r)-(n^4*p^3-3*n^4*p^2*r+3*n^4*p*r^2-n^4*r^3+4*n^3*p^4-12*n^3*p^3*r+12*n^3*p^2*r ^2-4*n^3*p*r^3+6*n^2*p^5-18*n^2*p^4*r+18*n^2*p^3*r^2-6*n^2*p^2*r^3+4*n*p^6-12*n *p^5*r+12*n*p^4*r^2-4*n*p^3*r^3+p^7-3*p^6*r+3*p^5*r^2-p^4*r^3-9*n^4*p^2+18*n^4* p*r-9*n^4*r^2-36*n^3*p^3+72*n^3*p^2*r-36*n^3*p*r^2-54*n^2*p^4+108*n^2*p^3*r-54* n^2*p^2*r^2-36*n*p^5+72*n*p^4*r-36*n*p^3*r^2-9*p^6+18*p^5*r-9*p^4*r^2+26*n^4*p-\ 26*n^4*r+104*n^3*p^2-104*n^3*p*r+156*n^2*p^3-156*n^2*p^2*r+104*n*p^4-104*n*p^3* r+26*p^5-26*p^4*r-24*n^4-96*n^3*p-144*n^2*p^2-96*n*p^3-24*p^4)/(n^4+4*n^3+6*n^2 +4*n+1)/(p-r-1)^3/(r+s)*A[n+1](r,s)+(4*n^4*p^5-20*n^4*p^4*r+40*n^4*p^3*r^2-40*n ^4*p^2*r^3+20*n^4*p*r^4-4*n^4*r^5+12*n^3*p^6-56*n^3*p^5*r+100*n^3*p^4*r^2-80*n^ 3*p^3*r^3+20*n^3*p^2*r^4+8*n^3*p*r^5-4*n^3*r^6+12*n^2*p^7-48*n^2*p^6*r+60*n^2*p ^5*r^2-60*n^2*p^3*r^4+48*n^2*p^2*r^5-12*n^2*p*r^6+4*n*p^8-8*n*p^7*r-20*n*p^6*r^ 2+80*n*p^5*r^3-100*n*p^4*r^4+56*n*p^3*r^5-12*n*p^2*r^6+4*p^8*r-20*p^7*r^2+40*p^ 6*r^3-40*p^5*r^4+20*p^4*r^5-4*p^3*r^6-46*n^4*p^4+184*n^4*p^3*r-276*n^4*p^2*r^2+ 184*n^4*p*r^3-46*n^4*r^4-140*n^3*p^5+516*n^3*p^4*r-664*n^3*p^3*r^2+296*n^3*p^2* r^3+36*n^3*p*r^4-44*n^3*r^5-138*n^2*p^6+408*n^2*p^5*r-246*n^2*p^4*r^2-336*n^2*p ^3*r^3+474*n^2*p^2*r^4-168*n^2*p*r^5+6*n^2*r^6-40*n*p^7+4*n*p^6*r+396*n*p^5*r^2 -824*n*p^4*r^3+656*n*p^3*r^4-204*n*p^2*r^5+12*n*p*r^6+4*p^8-72*p^7*r+254*p^6*r^ 2-376*p^5*r^3+264*p^4*r^4-80*p^3*r^5+6*p^2*r^6+202*n^4*p^3-606*n^4*p^2*r+606*n^ 4*p*r^2-202*n^4*r^3+624*n^3*p^4-1688*n^3*p^3*r+1320*n^3*p^2*r^2-72*n^3*p*r^3-\ 184*n^3*r^4+594*n^2*p^5-1098*n^2*p^4*r-336*n^2*p^3*r^2+1656*n^2*p^2*r^3-882*n^2 *p*r^4+66*n^2*r^5+120*n*p^6+468*n*p^5*r-2268*n*p^4*r^2+2800*n*p^3*r^3-1272*n*p^ 2*r^4+156*n*p*r^5-4*n*r^6-52*p^7+484*p^6*r-1218*p^5*r^2+1274*p^4*r^3-574*p^3*r^ 4+90*p^2*r^5-4*p*r^6-427*n^4*p^2+854*n^4*p*r-427*n^4*r^2-1332*n^3*p^3+2288*n^3* p^2*r-580*n^3*p*r^2-376*n^3*r^3-1158*n^2*p^4+636*n^2*p^3*r+2478*n^2*p^2*r^2-\ 2232*n^2*p*r^3+276*n^2*r^4+16*n*p^5-2396*n*p^4*r+5428*n*p^3*r^2-3776*n*p^2*r^3+ 772*n*p*r^4-44*n*r^5+270*p^6-1604*p^5*r+2812*p^4*r^2-1940*p^3*r^3+511*p^2*r^4-\ 50*p*r^5+r^6+441*n^4*p-441*n^4*r+1360*n^3*p^2-956*n^3*p*r-404*n^3*r^2+870*n^2*p ^3+1470*n^2*p^2*r-2904*n^2*p*r^2+564*n^2*r^3-760*n*p^4+4780*n*p^3*r-5700*n*p^2* r^2+1864*n*p*r^3-184*n*r^4-722*p^5+2850*p^4*r-3310*p^3*r^2+1410*p^2*r^3-239*p*r ^4+11*r^5-180*n^4-500*n^3*p-220*n^3*r+186*n^2*p^2-1872*n^2*p*r+606*n^2*r^2+1528 *n*p^3-4212*n*p^2*r+2340*n*p*r^2-376*n*r^3+1068*p^4-2744*p^3*r+2010*p^2*r^2-560 *p*r^3+46*r^4-48*n^3-474*n^2*p+330*n^2*r-1208*n*p^2+1468*n*p*r-404*n*r^2-876*p^ 3+1420*p^2*r-686*p*r^2+94*r^3+72*n^2+364*n*p-220*n*r+393*p^2-422*p*r+101*r^2-48 *n-103*p+55*r+12)/(n*p-n*r-n+p-r-1)/(n^3+3*n^2+3*n+1)/(p^2-2*p*r+r^2-3*p+3*r+2) ^2/(r+s)*diff(A[n+1](r,s),r)-(6*n^4*p^5-30*n^4*p^4*r+60*n^4*p^3*r^2-60*n^4*p^2* r^3+30*n^4*p*r^4-6*n^4*r^5+12*n^3*p^6-48*n^3*p^5*r+60*n^3*p^4*r^2-60*n^3*p^2*r^ 4+48*n^3*p*r^5-12*n^3*r^6+6*n^2*p^7-6*n^2*p^6*r-54*n^2*p^5*r^2+150*n^2*p^4*r^3-\ 150*n^2*p^3*r^4+54*n^2*p^2*r^5+6*n^2*p*r^6-6*n^2*r^7+12*n*p^7*r-48*n*p^6*r^2+60 *n*p^5*r^3-60*n*p^3*r^5+48*n*p^2*r^6-12*n*p*r^7+6*p^7*r^2-30*p^6*r^3+60*p^5*r^4 -60*p^4*r^5+30*p^3*r^6-6*p^2*r^7-72*n^4*p^4+288*n^4*p^3*r-432*n^4*p^2*r^2+288*n ^4*p*r^3-72*n^4*r^4-144*n^3*p^5+432*n^3*p^4*r-288*n^3*p^3*r^2-288*n^3*p^2*r^3+ 432*n^3*p*r^4-144*n^3*r^5-60*n^2*p^6-72*n^2*p^5*r+828*n^2*p^4*r^2-1392*n^2*p^3* r^3+828*n^2*p^2*r^4-72*n^2*p*r^5-60*n^2*r^6+12*n*p^7-204*n*p^6*r+540*n*p^5*r^2-\ 348*n*p^4*r^3-348*n*p^3*r^4+540*n*p^2*r^5-204*n*p*r^6+12*n*r^7+12*p^7*r-144*p^6 *r^2+468*p^5*r^3-672*p^4*r^4+468*p^3*r^5-144*p^2*r^6+12*p*r^7+333*n^4*p^3-999*n ^4*p^2*r+999*n^4*p*r^2-333*n^4*r^3+656*n^3*p^4-1292*n^3*p^3*r-60*n^3*p^2*r^2+ 1372*n^3*p*r^3-676*n^3*r^4+168*n^2*p^5+1128*n^2*p^4*r-4194*n^2*p^3*r^2+4134*n^2 *p^2*r^3-1038*n^2*p*r^4-198*n^2*r^5-156*n*p^6+1272*n*p^5*r-2052*n*p^4*r^2-60*n* p^3*r^3+2112*n*p^2*r^4-1260*n*p*r^5+144*n*r^6+6*p^7-198*p^6*r+1230*p^5*r^2-2734 *p^4*r^3+2719*p^3*r^4-1209*p^2*r^5+193*p*r^6-7*r^7-744*n^4*p^2+1488*n^4*p*r-744 *n^4*r^2-1388*n^3*p^3+1188*n^3*p^2*r+1788*n^3*p*r^2-1588*n^3*r^3+144*n^2*p^4-\ 4740*n^2*p^3*r+8892*n^2*p^2*r^2-4140*n^2*p*r^3-156*n^2*r^4+792*n*p^5-3672*n*p^4 *r+2604*n*p^3*r^2+3324*n*p^2*r^3-3732*n*p*r^4+684*n*r^5-84*p^6+1296*p^5*r-5076* p^4*r^2+7636*p^3*r^3-4896*p^2*r^4+1212*p*r^5-88*r^6+805*n^4*p-805*n^4*r+1252*n^ 3*p^2+716*n^3*p*r-1968*n^3*r^2-1548*n^2*p^3+8400*n^2*p^2*r-7326*n^2*p*r^2+474*n ^2*r^3-1968*n*p^4+4776*n*p^3*r+1236*n*p^2*r^2-5708*n*p*r^3+1664*n*r^4+474*p^5-\ 4338*p^4*r+11064*p^3*r^2-10652*p^2*r^3+3899*p*r^4-447*r^5-340*n^4-132*n^3*p-\ 1228*n^3*r+2796*n^2*p^2-5988*n^2*p*r+1152*n^2*r^2+2400*n*p^3-1608*n*p^2*r-4380* n*p*r^2+2228*n*r^3-1384*p^4+7936*p^3*r-12708*p^2*r^2+7012*p*r^3-1196*r^4-304*n^ 3-1842*n^2*p+930*n^2*r-1140*n*p^2-1404*n*p*r+1632*n*r^2+2227*p^3-7821*p^2*r+ 7119*p*r^2-1829*r^3+264*n^2-68*n*p+596*n*r-1940*p^2+3812*p*r-1608*r^2+80*n+837* p-757*r-148)/(n^2*p^2-2*n^2*p*r+n^2*r^2-3*n^2*p+3*n^2*r+2*n*p^2-4*n*p*r+2*n*r^2 +2*n^2-6*n*p+6*n*r+p^2-2*p*r+r^2+4*n-3*p+3*r+2)/(n^2+2*n+1)/(r+s)/(p^3-3*p^2*r+ 3*p*r^2-r^3-6*p^2+12*p*r-6*r^2+11*p-11*r-6)*diff(diff(A[n+1](r,s),r),r)+2*(2*n^ 4*p^3-6*n^4*p^2*r+6*n^4*p*r^2-2*n^4*r^3+2*n^3*p^4-12*n^3*p^2*r^2+16*n^3*p*r^3-6 *n^3*r^4+6*n^2*p^4*r-12*n^2*p^3*r^2+12*n^2*p*r^4-6*n^2*r^5+6*n*p^4*r^2-16*n*p^3 *r^3+12*n*p^2*r^4-2*n*r^6+2*p^4*r^3-6*p^3*r^4+6*p^2*r^5-2*p*r^6-15*n^4*p^2+30*n ^4*p*r-15*n^4*r^2-12*n^3*p^3-24*n^3*p^2*r+84*n^3*p*r^2-48*n^3*r^3+6*n^2*p^4-60* n^2*p^3*r+54*n^2*p^2*r^2+48*n^2*p*r^3-48*n^2*r^4+12*n*p^4*r-84*n*p^3*r^2+120*n* p^2*r^3-36*n*p*r^4-12*n*r^5+6*p^4*r^2-36*p^3*r^3+57*p^2*r^4-30*p*r^5+3*r^6+35*n ^4*p-35*n^4*r+10*n^3*p^2+120*n^3*p*r-130*n^3*r^2-48*n^2*p^3+174*n^2*p^2*r+6*n^2 *p*r^2-132*n^2*r^3+6*n*p^4-120*n*p^3*r+354*n*p^2*r^2-232*n*p*r^3-8*n*r^4+6*p^4* r-72*p^3*r^2+190*p^2*r^3-153*p*r^4+29*r^5-25*n^4+40*n^3*p-140*n^3*r+120*n^2*p^2 -120*n^2*p*r-150*n^2*r^2-52*n*p^3+396*n*p^2*r-516*n*p*r^2+72*n*r^3+2*p^4-60*p^3 *r+288*p^2*r^2-364*p*r^3+109*r^4-52*n^3-90*n^2*p-66*n^2*r+150*n*p^2-480*n*p*r+ 174*n*r^2-18*p^3+204*p^2*r-444*p*r^2+206*r^3-6*n^2-160*n*p+148*n*r+55*p^2-270*p *r+209*r^2+44*n-65*p+109*r+23)/(n^4*p^3-3*n^4*p^2*r+3*n^4*p*r^2-n^4*r^3-6*n^4*p ^2+12*n^4*p*r-6*n^4*r^2+4*n^3*p^3-12*n^3*p^2*r+12*n^3*p*r^2-4*n^3*r^3+11*n^4*p-\ 11*n^4*r-24*n^3*p^2+48*n^3*p*r-24*n^3*r^2+6*n^2*p^3-18*n^2*p^2*r+18*n^2*p*r^2-6 *n^2*r^3-6*n^4+44*n^3*p-44*n^3*r-36*n^2*p^2+72*n^2*p*r-36*n^2*r^2+4*n*p^3-12*n* p^2*r+12*n*p*r^2-4*n*r^3-24*n^3+66*n^2*p-66*n^2*r-24*n*p^2+48*n*p*r-24*n*r^2+p^ 3-3*p^2*r+3*p*r^2-r^3-36*n^2+44*n*p-44*n*r-6*p^2+12*p*r-6*r^2-24*n+11*p-11*r-6) /(r+s)*diff(diff(diff(A[n+1](r,s),r),r),r)-(n^4+4*n^3*r+6*n^2*r^2+4*n*r^3+r^4+4 *n^3+12*n^2*r+12*n*r^2+4*r^3+6*n^2+12*n*r+6*r^2+4*n+4*r+1)/(n^4+4*n^3+6*n^2+4*n +1)/(r+s)*diff(diff(diff(diff(A[n+1](r,s),r),r),r),r) = 0 -(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2-3*n-3*q+3*s+2)/(n+q-s)^2*A[n](r,s)+(3*n^3+9*n^2 *q-9*n^2*s+9*n*q^2-18*n*q*s+9*n*s^2+3*q^3-9*q^2*s+9*q*s^2-3*s^3-9*n^2-18*n*q+18 *n*s-9*q^2+18*q*s-9*s^2+7*n+7*q-7*s-2)/(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2-n-q+s)/(n +q-s)*diff(A[n](r,s),s)-(3*n^2+6*n*q-6*n*s+3*q^2-6*q*s+3*s^2-6*n-6*q+6*s+2)/(n^ 2+2*n*q-2*n*s+q^2-2*q*s+s^2-n-q+s)*diff(diff(A[n](r,s),s),s)+diff(diff(diff(A[n ](r,s),s),s),s)-(n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+3*n*s^2+q^3-3*q^2*s+3*q*s^ 2-s^3-3*n^2-6*n*q+6*n*s-3*q^2+6*q*s-3*s^2+2*n+2*q-2*s)*q^4/(n^4+4*n^3+6*n^2+4*n +1)/(q+n-s+1)^4*A[n+1](r,s)-(4*n^6*q^3+20*n^5*q^4-24*n^5*q^3*s+40*n^4*q^5-100*n ^4*q^4*s+60*n^4*q^3*s^2+40*n^3*q^6-160*n^3*q^5*s+200*n^3*q^4*s^2-80*n^3*q^3*s^3 +20*n^2*q^7-120*n^2*q^6*s+240*n^2*q^5*s^2-200*n^2*q^4*s^3+60*n^2*q^3*s^4+4*n*q^ 8-40*n*q^7*s+120*n*q^6*s^2-160*n*q^5*s^3+100*n*q^4*s^4-24*n*q^3*s^5-4*q^8*s+20* q^7*s^2-40*q^6*s^3+40*q^5*s^4-20*q^4*s^5+4*q^3*s^6-6*n^6*q^2-32*n^5*q^3+36*n^5* q^2*s-64*n^4*q^4+160*n^4*q^3*s-90*n^4*q^2*s^2-56*n^3*q^5+256*n^3*q^4*s-320*n^3* q^3*s^2+120*n^3*q^2*s^3-14*n^2*q^6+168*n^2*q^5*s-384*n^2*q^4*s^2+320*n^2*q^3*s^ 3-90*n^2*q^2*s^4+8*n*q^7+28*n*q^6*s-168*n*q^5*s^2+256*n*q^4*s^3-160*n*q^3*s^4+ 36*n*q^2*s^5+4*q^8-8*q^7*s-14*q^6*s^2+56*q^5*s^3-64*q^4*s^4+32*q^3*s^5-6*q^2*s^ 6+4*n^6*q+18*n^5*q^2-24*n^5*q*s+14*n^4*q^3-90*n^4*q^2*s+60*n^4*q*s^2-38*n^3*q^4 -56*n^3*q^3*s+180*n^3*q^2*s^2-80*n^3*q*s^3-78*n^2*q^5+114*n^2*q^4*s+84*n^2*q^3* s^2-180*n^2*q^2*s^3+60*n^2*q*s^4-52*n*q^6+156*n*q^5*s-114*n*q^4*s^2-56*n*q^3*s^ 3+90*n*q^2*s^4-24*n*q*s^5-12*q^7+52*q^6*s-78*q^5*s^2+38*q^4*s^3+14*q^3*s^4-18*q ^2*s^5+4*q*s^6-n^6-2*n^5*q+6*n^5*s+29*n^4*q^2+10*n^4*q*s-15*n^4*s^2+92*n^3*q^3-\ 116*n^3*q^2*s-20*n^3*q*s^2+20*n^3*s^3+96*n^2*q^4-276*n^2*q^3*s+174*n^2*q^2*s^2+ 20*n^2*q*s^3-15*n^2*s^4+36*n*q^5-192*n*q^4*s+276*n*q^3*s^2-116*n*q^2*s^3-10*n*q *s^4+6*n*s^5+2*q^6-36*q^5*s+96*q^4*s^2-92*q^3*s^3+29*q^2*s^4+2*q*s^5-s^6-n^5-21 *n^4*q+5*n^4*s-38*n^3*q^2+84*n^3*q*s-10*n^3*s^2+6*n^2*q^3+114*n^2*q^2*s-126*n^2 *q*s^2+10*n^2*s^3+42*n*q^4-12*n*q^3*s-114*n*q^2*s^2+84*n*q*s^3-5*n*s^4+18*q^5-\ 42*q^4*s+6*q^3*s^2+38*q^2*s^3-21*q*s^4+s^5+4*n^4-8*n^3*q-16*n^3*s-54*n^2*q^2+24 *n^2*q*s+24*n^2*s^2-48*n*q^3+108*n*q^2*s-24*n*q*s^2-16*n*s^3-8*q^4+48*q^3*s-54* q^2*s^2+8*q*s^3+4*s^4+6*n^3+22*n^2*q-18*n^2*s-4*n*q^2-44*n*q*s+18*n*s^2-12*q^3+ 4*q^2*s+22*q*s^2-6*s^3-n^2+18*n*q+2*n*s+7*q^2-18*q*s-s^2-5*n+3*q+5*s-2)/(q+n-s+ 1)^2/(n^5+n^4*q-n^4*s+5*n^4+4*n^3*q-4*n^3*s+10*n^3+6*n^2*q-6*n^2*s+10*n^2+4*n*q -4*n*s+5*n+q-s+1)/(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2+n+q-s)/(n+q-s)*diff(A[n+1](r,s ),s)-(6*n^7*q^2+30*n^6*q^3-42*n^6*q^2*s+60*n^5*q^4-180*n^5*q^3*s+126*n^5*q^2*s^ 2+60*n^4*q^5-300*n^4*q^4*s+450*n^4*q^3*s^2-210*n^4*q^2*s^3+30*n^3*q^6-240*n^3*q ^5*s+600*n^3*q^4*s^2-600*n^3*q^3*s^3+210*n^3*q^2*s^4+6*n^2*q^7-90*n^2*q^6*s+360 *n^2*q^5*s^2-600*n^2*q^4*s^3+450*n^2*q^3*s^4-126*n^2*q^2*s^5-12*n*q^7*s+90*n*q^ 6*s^2-240*n*q^5*s^3+300*n*q^4*s^4-180*n*q^3*s^5+42*n*q^2*s^6+6*q^7*s^2-30*q^6*s ^3+60*q^5*s^4-60*q^4*s^5+30*q^3*s^6-6*q^2*s^7-12*n^7*q-60*n^6*q^2+84*n^6*q*s-\ 108*n^5*q^3+360*n^5*q^2*s-252*n^5*q*s^2-72*n^4*q^4+540*n^4*q^3*s-900*n^4*q^2*s^ 2+420*n^4*q*s^3+12*n^3*q^5+288*n^3*q^4*s-1080*n^3*q^3*s^2+1200*n^3*q^2*s^3-420* n^3*q*s^4+36*n^2*q^6-36*n^2*q^5*s-432*n^2*q^4*s^2+1080*n^2*q^3*s^3-900*n^2*q^2* s^4+252*n^2*q*s^5+12*n*q^7-72*n*q^6*s+36*n*q^5*s^2+288*n*q^4*s^3-540*n*q^3*s^4+ 360*n*q^2*s^5-84*n*q*s^6-12*q^7*s+36*q^6*s^2-12*q^5*s^3-72*q^4*s^4+108*q^3*s^5-\ 60*q^2*s^6+12*q*s^7+7*n^7+25*n^6*q-49*n^6*s-15*n^5*q^2-150*n^5*q*s+147*n^5*s^2-\ 161*n^4*q^3+75*n^4*q^2*s+375*n^4*q*s^2-245*n^4*s^3-242*n^3*q^4+644*n^3*q^3*s-\ 150*n^3*q^2*s^2-500*n^3*q*s^3+245*n^3*s^4-138*n^2*q^5+726*n^2*q^4*s-966*n^2*q^3 *s^2+150*n^2*q^2*s^3+375*n^2*q*s^4-147*n^2*s^5-18*n*q^6+276*n*q^5*s-726*n*q^4*s ^2+644*n*q^3*s^3-75*n*q^2*s^4-150*n*q*s^5+49*n*s^6+6*q^7+18*q^6*s-138*q^5*s^2+ 242*q^4*s^3-161*q^3*s^4+15*q^2*s^5+25*q*s^6-7*s^7+10*n^6+96*n^5*q-60*n^5*s+234* n^4*q^2-480*n^4*q*s+150*n^4*s^2+196*n^3*q^3-936*n^3*q^2*s+960*n^3*q*s^2-200*n^3 *s^3-588*n^2*q^3*s+1404*n^2*q^2*s^2-960*n^2*q*s^3+150*n^2*s^4-72*n*q^5+588*n*q^ 3*s^2-936*n*q^2*s^3+480*n*q*s^4-60*n*s^5-24*q^6+72*q^5*s-196*q^3*s^3+234*q^2*s^ 4-96*q*s^5+10*s^6-21*n^5-n^4*q+105*n^4*s+164*n^3*q^2+4*n^3*q*s-210*n^3*s^2+264* n^2*q^3-492*n^2*q^2*s-6*n^2*q*s^2+210*n^2*s^3+138*n*q^4-528*n*q^3*s+492*n*q^2*s ^2+4*n*q*s^3-105*n*s^4+18*q^5-138*q^4*s+264*q^3*s^2-164*q^2*s^3-q*s^4+21*s^5-46 *n^4-140*n^3*q+184*n^3*s-108*n^2*q^2+420*n^2*q*s-276*n^2*s^2+16*n*q^3+216*n*q^2 *s-420*n*q*s^2+184*n*s^3+28*q^4-16*q^3*s-108*q^2*s^2+140*q*s^3-46*s^4-19*n^3-81 *n^2*q+57*n^2*s-99*n*q^2+162*n*q*s-57*n*s^2-29*q^3+99*q^2*s-81*q*s^2+19*s^3+6*n ^2+8*n*q-12*n*s-10*q^2-8*q*s+6*s^2+n+9*q-s-2)/(n^6+2*n^5*q-2*n^5*s+n^4*q^2-2*n^ 4*q*s+n^4*s^2+5*n^5+9*n^4*q-9*n^4*s+4*n^3*q^2-8*n^3*q*s+4*n^3*s^2+10*n^4+16*n^3 *q-16*n^3*s+6*n^2*q^2-12*n^2*q*s+6*n^2*s^2+10*n^3+14*n^2*q-14*n^2*s+4*n*q^2-8*n *q*s+4*n*s^2+5*n^2+6*n*q-6*n*s+q^2-2*q*s+s^2+n+q-s)/(q+n-s+1)^2/(n^2+2*n*q-2*n* s+q^2-2*q*s+s^2-n-q+s)*diff(diff(A[n+1](r,s),s),s)-2*(2*n^6*q+6*n^5*q^2-12*n^5* q*s+6*n^4*q^3-30*n^4*q^2*s+30*n^4*q*s^2+2*n^3*q^4-24*n^3*q^3*s+60*n^3*q^2*s^2-\ 40*n^3*q*s^3-6*n^2*q^4*s+36*n^2*q^3*s^2-60*n^2*q^2*s^3+30*n^2*q*s^4+6*n*q^4*s^2 -24*n*q^3*s^3+30*n*q^2*s^4-12*n*q*s^5-2*q^4*s^3+6*q^3*s^4-6*q^2*s^5+2*q*s^6-3*n ^6-6*n^5*q+18*n^5*s+3*n^4*q^2+30*n^4*q*s-45*n^4*s^2+12*n^3*q^3-12*n^3*q^2*s-60* n^3*q*s^2+60*n^3*s^3+6*n^2*q^4-36*n^2*q^3*s+18*n^2*q^2*s^2+60*n^2*q*s^3-45*n^2* s^4-12*n*q^4*s+36*n*q^3*s^2-12*n*q^2*s^3-30*n*q*s^4+18*n*s^5+6*q^4*s^2-12*q^3*s ^3+3*q^2*s^4+6*q*s^5-3*s^6-7*n^5-27*n^4*q+35*n^4*s-26*n^3*q^2+108*n^3*q*s-70*n^ 3*s^2+78*n^2*q^2*s-162*n^2*q*s^2+70*n^2*s^3+6*n*q^4-78*n*q^2*s^2+108*n*q*s^3-35 *n*s^4-6*q^4*s+26*q^2*s^3-27*q*s^4+7*s^5+n^4-20*n^3*q-4*n^3*s-36*n^2*q^2+60*n^2 *q*s+6*n^2*s^2-12*n*q^3+72*n*q^2*s-60*n*q*s^2-4*n*s^3+2*q^4+12*q^3*s-36*q^2*s^2 +20*q*s^3+s^4+14*n^3+12*n^2*q-42*n^2*s-12*n*q^2-24*n*q*s+42*n*s^2-6*q^3+12*q^2* s+12*q*s^2-14*s^3+11*n^2+18*n*q-22*n*s+q^2-18*q*s+11*s^2+n+5*q-s-1)/(n^7+3*n^6* q-3*n^6*s+3*n^5*q^2-6*n^5*q*s+3*n^5*s^2+n^4*q^3-3*n^4*q^2*s+3*n^4*q*s^2-n^4*s^3 +4*n^6+12*n^5*q-12*n^5*s+12*n^4*q^2-24*n^4*q*s+12*n^4*s^2+4*n^3*q^3-12*n^3*q^2* s+12*n^3*q*s^2-4*n^3*s^3+5*n^5+17*n^4*q-17*n^4*s+18*n^3*q^2-36*n^3*q*s+18*n^3*s ^2+6*n^2*q^3-18*n^2*q^2*s+18*n^2*q*s^2-6*n^2*s^3+8*n^3*q-8*n^3*s+12*n^2*q^2-24* n^2*q*s+12*n^2*s^2+4*n*q^3-12*n*q^2*s+12*n*q*s^2-4*n*s^3-5*n^3-3*n^2*q+3*n^2*s+ 3*n*q^2-6*n*q*s+3*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-4*n^2-4*n*q+4*n*s-n-q+s)/(q+n-s +1)*diff(diff(diff(A[n+1](r,s),s),s),s)-(n^4-4*n^3*s+6*n^2*s^2-4*n*s^3+s^4+4*n^ 3-12*n^2*s+12*n*s^2-4*s^3+6*n^2-12*n*s+6*s^2+4*n-4*s+1)/(n^5+n^4*q-n^4*s+5*n^4+ 4*n^3*q-4*n^3*s+10*n^3+6*n^2*q-6*n^2*s+10*n^2+4*n*q-4*n*s+5*n+q-s+1)*diff(diff( diff(diff(A[n+1](r,s),s),s),s),s) = 0 ------------------------------------------------- This took, 0.669, seconds. -------------------------------------------- Theorem: define the Abel-sum type sequence by n ----- \ 5 (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)^5*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s 5 4 4 3 2 3 2 3 2 2 4 - (p - 4 p r + p s + 6 p r - 4 p r s - 4 p r + 6 p r s + p r 3 4 4 3 3 2 2 2 - 4 p r s + r s - 15 p + 46 p r - 14 p s - 48 p r + 42 p r s 3 2 4 3 3 2 2 + 18 p r - 42 p r s - r + 14 r s + 85 p - 184 p r + 71 p s 2 3 2 2 + 113 p r - 142 p r s - 14 r + 71 r s - 225 p + 296 p r - 154 p s 2 / - 71 r + 154 r s + 274 p - 154 r + 120 s - 120) A[n](r, s) / ( / 2 3 8 7 7 (p r + p s - r - r s - r - s) (p - r - 1) ) + (4 p - 27 p r + 5 p s 6 2 6 5 3 5 2 4 4 4 3 + 77 p r - 35 p r s - 119 p r + 105 p r s + 105 p r - 175 p r s 3 5 3 4 2 6 2 5 7 6 8 - 49 p r + 175 p r s + 7 p r - 105 p r s + 3 p r + 35 p r s - r 7 7 6 6 5 2 5 - 5 r s - 78 p + 456 p r - 90 p s - 1098 p r + 540 p r s 4 3 4 2 3 4 3 3 2 5 + 1380 p r - 1350 p r s - 930 p r + 1800 p r s + 288 p r 2 4 6 5 7 6 6 - 1350 p r s - 6 p r + 540 p r s - 12 r - 90 r s + 638 p 5 5 4 2 4 3 3 - 3163 p r + 665 p s + 6245 p r - 3325 p r s - 6110 p r 3 2 2 4 2 3 5 4 + 6650 p r s + 2920 p r - 6650 p r s - 503 p r + 3325 p r s 6 5 5 4 4 3 2 - 27 r - 665 r s - 2865 p + 11700 p r - 2625 p s - 18150 p r 3 2 3 2 2 4 3 + 10500 p r s + 12900 p r - 15750 p r s - 3825 p r + 10500 p r s 5 4 4 3 3 2 2 + 240 r - 2625 r s + 7751 p - 24983 p r + 6021 p s + 28443 p r 2 3 2 4 3 - 18063 p r s - 12941 p r + 18063 p r s + 1730 r - 6021 r s 3 2 2 2 3 - 12987 p + 30864 p r - 8097 p s - 22767 p r + 16194 p r s + 4890 r 2 2 2 - 8097 r s + 13207 p - 20457 p r + 5957 p s + 7250 r - 5957 r s /d \ / 2 - 7470 p + 5610 r - 1860 s + 1800) |-- A[n](r, s)| / ((p - r - 1) (p r \dr / / 2 2 3 2 2 + p s - 2 p r - 2 p r s + r + r s - 3 p r - 3 p s + 3 r + 3 r s + 2 r 2 2 2 9 8 8 + 2 s) (p - 2 p r + r - 3 p + 3 r + 2) ) - (6 p - 44 p r + 10 p s 7 2 7 6 3 6 2 5 4 + 136 p r - 80 p r s - 224 p r + 280 p r s + 196 p r 5 3 4 5 4 4 3 6 3 5 2 7 - 560 p r s - 56 p r + 700 p r s - 56 p r - 560 p r s + 64 p r 2 6 8 7 9 8 8 7 + 280 p r s - 26 p r - 80 p r s + 4 r + 10 r s - 138 p + 894 p r 7 6 2 6 5 3 5 2 - 210 p s - 2394 p r + 1470 p r s + 3318 p r - 4410 p r s 4 4 4 3 3 5 3 4 2 6 - 2310 p r + 7350 p r s + 378 p r - 7350 p r s + 546 p r 2 5 7 6 8 7 7 + 4410 p r s - 366 p r - 1470 p r s + 72 r + 210 r s + 1371 p 6 6 5 2 5 4 3 - 7722 p r + 1875 p s + 17541 p r - 11250 p r s - 19860 p r 4 2 3 4 3 3 2 5 2 4 + 28125 p r s + 10485 p r - 37500 p r s - 666 p r + 28125 p r s 6 5 7 6 6 5 - 1653 p r - 11250 p r s + 504 r + 1875 r s - 7725 p + 37035 p r 5 4 2 4 3 3 3 2 - 9315 p s - 69300 p r + 46575 p r s + 61350 p r - 93150 p r s 2 4 2 3 5 4 6 - 22725 p r + 93150 p r s - 225 p r - 46575 p r s + 1590 r 5 5 4 4 3 2 + 9315 r s + 27214 p - 107846 p r + 28224 p s + 159244 p r 3 2 3 2 2 4 - 112896 p r s - 102796 p r + 169344 p r s + 23174 p r 3 5 4 4 3 - 112896 p r s + 1010 r + 28224 r s - 62172 p + 195156 p r 3 2 2 2 3 2 - 53532 p s - 212436 p r + 160596 p r s + 88092 p r - 160596 p r s 4 3 3 2 2 2 - 8640 r + 53532 r s + 92119 p - 214118 p r + 62239 p s + 151879 p r 3 2 2 - 124478 p r s - 29880 r + 62239 r s - 85365 p + 130035 p r - 40695 p s 2 - 44670 r + 40695 r s + 44890 p - 33390 r + 11500 s - 10200) / 2 \ |d | / 2 2 3 3 |--- A[n](r, s)| / ((p - 2 p r + r - 3 p + 3 r + 2) %1 (p r + p s | 2 | / \dr / 2 2 2 3 2 4 3 2 2 - 3 p r - 3 p r s + 3 p r + 3 p r s - r - r s - 6 p r - 6 p s 2 3 2 2 + 12 p r + 12 p r s - 6 r - 6 r s + 11 p r + 11 p s - 11 r - 11 r s 8 7 7 6 2 6 - 6 r - 6 s)) + (4 p - 22 p r + 10 p s + 42 p r - 70 p r s 5 3 5 2 4 4 4 3 3 5 - 14 p r + 210 p r s - 70 p r - 350 p r s + 126 p r 3 4 2 6 2 5 7 6 8 + 350 p r s - 98 p r - 210 p r s + 38 p r + 70 p r s - 6 r 7 7 6 6 5 2 5 - 10 r s - 90 p + 430 p r - 200 p s - 690 p r + 1200 p r s 4 3 4 2 3 4 3 3 2 5 + 150 p r - 3000 p r s + 850 p r + 4000 p r s - 1110 p r 2 4 6 5 7 6 6 - 3000 p r s + 570 p r + 1200 p r s - 110 r - 200 r s + 860 p 5 5 4 2 4 3 3 - 3495 p r + 1665 p s + 4575 p r - 8325 p r s - 550 p r 3 2 2 4 2 3 5 4 + 16650 p r s - 3750 p r - 16650 p r s + 3165 p r + 8325 p r s 6 5 5 4 4 3 2 - 805 r - 1665 r s - 4550 p + 15275 p r - 7475 p s - 15600 p r 3 2 3 2 2 4 3 + 29900 p r s + 650 p r - 44850 p r s + 7150 p r + 29900 p r s 5 4 4 3 3 2 2 - 2925 r - 7475 r s + 14546 p - 38653 p r + 19531 p s + 28683 p r 2 3 2 4 3 3 - 58593 p r s + 409 p r + 58593 p r s - 4985 r - 19531 r s - 28700 p 2 2 2 3 2 + 56415 p r - 29685 p s - 26730 p r + 59370 p r s - 985 r - 29685 r s 2 2 + 34030 p - 43750 p r + 24310 p s + 9720 r - 24310 r s - 22100 p / 3 \ |d | / 4 4 3 2 + 13800 r - 8300 s + 6000) |--- A[n](r, s)| / ((p r + p s - 4 p r | 3 | / \dr / 3 2 3 2 2 4 3 5 4 3 - 4 p r s + 6 p r + 6 p r s - 4 p r - 4 p r s + r + r s - 10 p r 3 2 2 2 3 2 4 3 - 10 p s + 30 p r + 30 p r s - 30 p r - 30 p r s + 10 r + 10 r s 2 2 2 3 2 + 35 p r + 35 p s - 70 p r - 70 p r s + 35 r + 35 r s - 50 p r 2 5 4 3 2 - 50 p s + 50 r + 50 r s + 24 r + 24 s) %1) - (p + 5 p s - 10 p r 3 2 3 2 2 4 3 5 4 - 20 p r s + 20 p r + 30 p r s - 15 p r - 20 p r s + 4 r + 5 r s 4 3 2 2 2 3 2 4 - 15 p - 60 p s + 90 p r + 180 p r s - 120 p r - 180 p r s + 45 r 3 3 2 2 3 2 + 60 r s + 85 p + 255 p s - 255 p r - 510 p r s + 170 r + 255 r s 2 2 - 225 p - 450 p s + 225 r + 450 r s + 274 p + 274 s - 120) / 4 \ |d | / 4 4 3 2 3 2 3 |--- A[n](r, s)| / (p r + p s - 4 p r - 4 p r s + 6 p r | 4 | / \dr / 2 2 4 3 5 4 3 3 2 2 + 6 p r s - 4 p r - 4 p r s + r + r s - 10 p r - 10 p s + 30 p r 2 3 2 4 3 2 2 + 30 p r s - 30 p r - 30 p r s + 10 r + 10 r s + 35 p r + 35 p s 2 3 2 2 - 70 p r - 70 p r s + 35 r + 35 r s - 50 p r - 50 p s + 50 r + 50 r s / 5 \ |d | 5 4 5 3 5 2 2 + 24 r + 24 s) + |--- A[n](r, s)| + (n p - 4 n p r + 6 n p r | 5 | \dr / 5 3 5 4 4 5 4 4 4 3 2 4 2 3 - 4 n p r + n r + 5 n p - 20 n p r + 30 n p r - 20 n p r 4 4 3 6 3 5 3 4 2 3 3 3 + 5 n p r + 10 n p - 40 n p r + 60 n p r - 40 n p r 3 2 4 2 7 2 6 2 5 2 2 4 3 + 10 n p r + 10 n p - 40 n p r + 60 n p r - 40 n p r 2 3 4 8 7 6 2 5 3 4 4 + 10 n p r + 5 n p - 20 n p r + 30 n p r - 20 n p r + 5 n p r 9 8 7 2 6 3 5 4 5 3 5 2 + p - 4 p r + 6 p r - 4 p r + p r - 14 n p + 42 n p r 5 2 5 3 4 4 4 3 4 2 2 - 42 n p r + 14 n r - 70 n p + 210 n p r - 210 n p r 4 3 3 5 3 4 3 3 2 3 2 3 + 70 n p r - 140 n p + 420 n p r - 420 n p r + 140 n p r 2 6 2 5 2 4 2 2 3 3 7 - 140 n p + 420 n p r - 420 n p r + 140 n p r - 70 n p 6 5 2 4 3 8 7 6 2 + 210 n p r - 210 n p r + 70 n p r - 14 p + 42 p r - 42 p r 5 3 5 2 5 5 2 4 3 4 2 + 14 p r + 71 n p - 142 n p r + 71 n r + 355 n p - 710 n p r 4 2 3 4 3 3 3 2 2 2 5 + 355 n p r + 710 n p - 1420 n p r + 710 n p r + 710 n p 2 4 2 3 2 6 5 4 2 - 1420 n p r + 710 n p r + 355 n p - 710 n p r + 355 n p r 7 6 5 2 5 5 4 2 + 71 p - 142 p r + 71 p r - 154 n p + 154 n r - 770 n p 4 3 3 3 2 2 4 2 3 + 770 n p r - 1540 n p + 1540 n p r - 1540 n p + 1540 n p r 5 4 6 5 5 4 - 770 n p + 770 n p r - 154 p + 154 p r + 120 n + 600 n p 3 2 2 3 4 5 / + 1200 n p + 1200 n p + 600 n p + 120 p ) A[n + 1](r, s) / ( / 5 4 3 2 4 5 7 (n + 5 n + 10 n + 10 n + 5 n + 1) (p - r - 1) (r + s)) - (5 n p 5 6 5 5 2 5 4 3 5 3 4 5 2 5 - 35 n p r + 105 n p r - 175 n p r + 175 n p r - 105 n p r 5 6 5 7 4 8 4 7 4 6 2 + 35 n p r - 5 n r + 20 n p - 135 n p r + 385 n p r 4 5 3 4 4 4 4 3 5 4 2 6 4 7 - 595 n p r + 525 n p r - 245 n p r + 35 n p r + 15 n p r 4 8 3 9 3 8 3 7 2 3 6 3 - 5 n r + 30 n p - 190 n p r + 490 n p r - 630 n p r 3 5 4 3 4 5 3 3 6 3 2 7 3 8 + 350 n p r + 70 n p r - 210 n p r + 110 n p r - 20 n p r 2 10 2 9 2 8 2 2 7 3 2 6 4 + 20 n p - 110 n p r + 210 n p r - 70 n p r - 350 n p r 2 5 5 2 4 6 2 3 7 2 2 8 11 + 630 n p r - 490 n p r + 190 n p r - 30 n p r + 5 n p 10 9 2 8 3 7 4 6 5 - 15 n p r - 35 n p r + 245 n p r - 525 n p r + 595 n p r 5 6 4 7 3 8 11 10 2 9 3 - 385 n p r + 135 n p r - 20 n p r + 5 p r - 35 p r + 105 p r 8 4 7 5 6 6 5 7 4 8 5 6 - 175 p r + 175 p r - 105 p r + 35 p r - 5 p r - 90 n p 5 5 5 4 2 5 3 3 5 2 4 + 540 n p r - 1350 n p r + 1800 n p r - 1350 n p r 5 5 5 6 4 7 4 6 4 5 2 + 540 n p r - 90 n r - 365 n p + 2105 n p r - 4965 n p r 4 4 3 4 3 4 4 2 5 4 6 4 7 + 6025 n p r - 3775 n p r + 915 n p r + 145 n p r - 85 n r 3 8 3 7 3 6 2 3 5 3 3 4 4 - 550 n p + 2940 n p r - 6080 n p r + 5540 n p r - 900 n p r 3 3 5 3 2 6 3 7 3 8 2 9 - 2300 n p r + 1760 n p r - 420 n p r + 10 n r - 360 n p 2 8 2 7 2 2 6 3 2 5 4 + 1590 n p r - 1950 n p r - 1530 n p r + 6450 n p r 2 4 5 2 3 6 2 2 7 2 8 10 - 6990 n p r + 3510 n p r - 750 n p r + 30 n p r - 80 n p 9 8 2 7 3 6 4 5 5 + 80 n p r + 1230 n p r - 4580 n p r + 7250 n p r - 6120 n p r 4 6 3 7 2 8 11 10 9 2 + 2770 n p r - 580 n p r + 30 n p r + 5 p - 135 p r + 715 p r 8 3 7 4 6 5 5 6 4 7 3 8 - 1735 p r + 2325 p r - 1805 p r + 785 p r - 165 p r + 10 p r 5 5 5 4 5 3 2 5 2 3 5 4 + 665 n p - 3325 n p r + 6650 n p r - 6650 n p r + 3325 n p r 5 5 4 6 4 5 4 4 2 4 3 3 - 665 n r + 2740 n p - 13115 n p r + 24475 n p r - 21550 n p r 4 2 4 4 5 4 6 3 7 3 6 + 7850 n p r + 185 n p r - 585 n r + 4140 n p - 18020 n p r 3 5 2 3 4 3 3 3 4 3 2 5 + 27830 n p r - 13750 n p r - 7800 n p r + 10960 n p r 3 6 3 7 2 8 2 7 2 6 2 - 3530 n p r + 170 n r + 2620 n p - 8540 n p r + 2860 n p r 2 5 3 2 4 4 2 3 5 2 2 6 + 22110 n p r - 37950 n p r + 25680 n p r - 7360 n p r 2 7 2 8 9 8 7 2 + 590 n p r - 10 n r + 455 n p + 1145 n p r - 13120 n p r 6 3 5 4 4 5 3 6 + 32520 n p r - 37725 n p r + 22545 n p r - 6470 n p r 2 7 8 10 9 8 2 7 3 + 670 n p r - 20 n p r - 100 p + 1455 p r - 5975 p r + 11560 p r 6 4 5 5 4 6 3 7 2 8 - 12100 p r + 6975 p r - 2055 p r + 250 p r - 10 p r 5 4 5 3 5 2 2 5 3 5 4 - 2625 n p + 10500 n p r - 15750 n p r + 10500 n p r - 2625 n r 4 5 4 4 4 3 2 4 2 3 - 11000 n p + 41875 n p r - 57500 n p r + 31250 n p r 4 4 4 5 3 6 3 5 3 4 2 - 2500 n p r - 2125 n r - 16580 n p + 55480 n p r - 54950 n p r 3 3 3 3 2 4 3 5 3 6 2 7 - 3400 n p r + 33800 n p r - 15520 n p r + 1170 n r - 9820 n p 2 6 2 5 2 2 4 3 2 3 4 + 19000 n p r + 26220 n p r - 98650 n p r + 96100 n p r 2 2 5 2 6 2 7 8 7 - 37380 n p r + 4700 n p r - 170 n r - 770 n p - 13480 n p r 6 2 5 3 4 4 3 5 + 66180 n p r - 114880 n p r + 94275 n p r - 36980 n p r 2 6 7 8 9 8 7 2 + 6030 n p r - 380 n p r + 5 n r + 845 p - 8375 p r + 26760 p r 6 3 5 4 4 5 3 6 2 7 - 40380 p r + 31850 p r - 12995 p r + 2500 p r - 210 p r 8 5 3 5 2 5 2 5 3 + 5 p r + 6021 n p - 18063 n p r + 18063 n p r - 6021 n r 4 4 4 3 4 2 2 4 3 + 25630 n p - 72415 n p r + 63465 n p r - 12205 n p r 4 4 3 5 3 4 3 3 2 - 4475 n r + 38060 n p - 87780 n p r + 30730 n p r 3 2 3 3 4 3 5 2 6 2 5 + 53890 n p r - 39150 n p r + 4250 n r + 19440 n p - 2460 n p r 2 4 2 2 3 3 2 2 4 2 5 - 125520 n p r + 198090 n p r - 108150 n p r + 19770 n p r 2 6 7 6 5 2 4 3 - 1170 n r - 2970 n p + 59670 n p r - 181470 n p r + 218770 n p r 3 4 2 5 6 7 8 - 119725 n p r + 28575 n p r - 2935 n p r + 85 n r - 3960 p 7 6 2 5 3 4 4 3 5 + 28710 p r - 70650 p r + 80810 p r - 46320 p r + 13111 p r 2 6 7 8 5 2 5 5 2 - 1793 p r + 93 p r - r - 8097 n p + 16194 n p r - 8097 n r 4 3 4 2 4 2 4 3 3 4 - 34830 n p + 64005 n p r - 23520 n p r - 5655 n r - 49400 n p 3 3 3 2 2 3 3 3 4 + 58280 n p r + 40590 n p r - 58420 n p r + 8950 n r 2 5 2 4 2 3 2 2 2 3 - 15940 n p - 68500 n p r + 224420 n p r - 183830 n p r 2 4 2 5 6 5 4 2 + 48100 n p r - 4250 n r + 18070 n p - 140300 n p r + 282250 n p r 3 3 2 4 5 6 7 - 226720 n p r + 78125 n p r - 12010 n p r + 585 n r + 11360 p 6 5 2 4 3 3 4 2 5 - 61450 p r + 114200 p r - 96250 p r + 39570 p r - 8117 p r 6 7 5 5 4 2 4 + 704 p r - 17 r + 5957 n p - 5957 n r + 25550 n p - 21315 n p r 4 2 3 3 3 2 3 2 3 3 - 4235 n r + 31320 n p + 8240 n p r - 50870 n p r + 11310 n r 2 4 2 3 2 2 2 2 3 - 8720 n p + 128840 n p r - 180900 n p r + 69730 n p r 2 4 5 4 3 2 - 8950 n r - 41110 n p + 188110 n p r - 247380 n p r 2 3 4 5 6 5 + 126780 n p r - 28525 n p r + 2125 n r - 20780 p + 83570 p r 4 2 3 3 2 4 5 6 5 - 114870 p r + 70700 p r - 21330 p r + 2827 p r - 117 r - 1860 n 4 4 3 2 3 3 2 - 7565 n p - 1735 n r - 3190 n p - 23880 n p r + 8470 n r 2 3 2 2 2 2 2 3 4 + 28530 n p - 95160 n p r + 59340 n p r - 11310 n r + 50145 n p 3 2 2 3 4 5 - 143520 n p r + 120120 n p r - 40520 n p r + 4475 n r + 24555 p 4 3 2 2 3 4 5 4 - 72630 p r + 73500 p r - 33460 p r + 6600 p r - 425 r - 300 n 3 3 2 2 2 2 2 - 4670 n p + 3470 n r - 20680 n p + 27350 n p r - 8470 n r 3 2 2 3 4 - 34205 n p + 61255 n p r - 33905 n p r + 5655 n r - 18790 p 3 2 2 3 4 3 2 + 40955 p r - 30805 p r + 9235 p r - 895 r + 600 n + 5270 n p 2 2 2 3 2 - 3470 n r + 12975 n p - 15410 n p r + 4235 n r + 9436 p - 15333 p r 2 3 2 2 + 7628 p r - 1131 r - 600 n - 2935 n p + 1735 n r - 3182 p + 3429 p r 2 /d \ / - 847 r + 300 n + 647 p - 347 r - 60) |-- A[n + 1](r, s)| / ( \dr / / 4 3 2 (n p - n r - n + p - r - 1) (n + 4 n + 6 n + 4 n + 1) 2 2 3 5 8 5 7 (p - 2 p r + r - 3 p + 3 r + 2) (r + s)) + (10 n p - 80 n p r 5 6 2 5 5 3 5 4 4 5 3 5 5 2 6 + 280 n p r - 560 n p r + 700 n p r - 560 n p r + 280 n p r 5 7 5 8 4 9 4 8 4 7 2 - 80 n p r + 10 n r + 30 n p - 220 n p r + 680 n p r 4 6 3 4 5 4 4 4 5 4 3 6 - 1120 n p r + 980 n p r - 280 n p r - 280 n p r 4 2 7 4 8 4 9 3 10 3 9 + 320 n p r - 130 n p r + 20 n r + 30 n p - 180 n p r 3 8 2 3 7 3 3 6 4 3 5 5 + 370 n p r - 80 n p r - 980 n p r + 1960 n p r 3 4 6 3 3 7 3 2 8 3 9 3 10 - 1820 n p r + 880 n p r - 170 n p r - 20 n p r + 10 n r 2 11 2 10 2 9 2 2 8 3 2 7 4 + 10 n p - 20 n p r - 170 n p r + 880 n p r - 1820 n p r 2 6 5 2 5 6 2 4 7 2 3 8 2 2 9 + 1960 n p r - 980 n p r - 80 n p r + 370 n p r - 180 n p r 2 10 11 10 2 9 3 8 4 + 30 n p r + 20 n p r - 130 n p r + 320 n p r - 280 n p r 7 5 6 6 5 7 4 8 3 9 - 280 n p r + 980 n p r - 1120 n p r + 680 n p r - 220 n p r 2 10 11 2 10 3 9 4 8 5 7 6 + 30 n p r + 10 p r - 80 p r + 280 p r - 560 p r + 700 p r 6 7 5 8 4 9 3 10 5 7 5 6 - 560 p r + 280 p r - 80 p r + 10 p r - 210 n p + 1470 n p r 5 5 2 5 4 3 5 3 4 5 2 5 - 4410 n p r + 7350 n p r - 7350 n p r + 4410 n p r 5 6 5 7 4 8 4 7 4 6 2 - 1470 n p r + 210 n r - 640 n p + 4070 n p r - 10570 n p r 4 5 3 4 4 4 4 3 5 4 2 6 + 13790 n p r - 8050 n p r - 910 n p r + 4130 n p r 4 7 4 8 3 9 3 8 3 7 2 - 2230 n p r + 410 n r - 630 n p + 3110 n p r - 4300 n p r 3 6 3 3 5 4 3 4 5 3 3 6 - 4060 n p r + 19880 n p r - 26320 n p r + 16940 n p r 3 2 7 3 8 3 9 2 10 2 9 - 4900 n p r + 110 n p r + 170 n r - 180 n p - 90 n p r 2 8 2 2 7 3 2 6 4 2 5 5 + 5070 n p r - 17820 n p r + 28140 n p r - 21840 n p r 2 4 6 2 3 7 2 2 8 2 9 2 10 + 5040 n p r + 4380 n p r - 3480 n p r + 810 n p r - 30 n r 11 10 9 2 8 3 7 4 + 20 n p - 580 n p r + 2810 n p r - 5050 n p r + 1190 n p r 6 5 5 6 4 7 3 8 + 9590 n p r - 16870 n p r + 13490 n p r - 5650 n p r 2 9 10 11 10 2 9 3 + 1110 n p r - 60 n p r + 20 p r - 400 p r + 2270 p r 8 4 7 5 6 6 5 7 4 8 - 6370 p r + 10430 p r - 10570 p r + 6650 p r - 2470 p r 3 9 2 10 5 6 5 5 5 4 2 + 470 p r - 30 p r + 1875 n p - 11250 n p r + 28125 n p r 5 3 3 5 2 4 5 5 5 6 - 37500 n p r + 28125 n p r - 11250 n p r + 1875 n r 4 7 4 6 4 5 2 4 4 3 + 5805 n p - 31260 n p r + 65655 n p r - 62550 n p r 4 3 4 4 2 5 4 6 4 7 + 15675 n p r + 18720 n p r - 15615 n p r + 3570 n r 3 8 3 7 3 6 2 3 5 3 + 5550 n p - 21180 n p r + 11610 n p r + 64320 n p r 3 4 4 3 3 5 3 2 6 3 7 - 142950 n p r + 126900 n p r - 50970 n p r + 5640 n p r 3 8 2 9 2 8 2 7 2 + 1080 n r + 1160 n p + 6210 n p r - 56610 n p r 2 6 3 2 5 4 2 4 5 2 3 6 + 143700 n p r - 167310 n p r + 81540 n p r + 9090 n p r 2 2 7 2 8 2 9 10 9 - 25740 n p r + 8550 n p r - 590 n r - 450 n p + 6820 n p r 8 2 7 3 6 4 5 5 - 24480 n p r + 27540 n p r + 23655 n p r - 95310 n p r 4 6 3 7 2 8 9 10 + 106605 n p r - 58320 n p r + 15435 n p r - 1530 n p r + 35 n r 11 10 9 2 8 3 7 4 + 10 p - 560 p r + 6210 p r - 26790 p r + 60465 p r 6 5 5 6 4 7 3 8 2 9 - 79920 p r + 64035 p r - 30510 p r + 7965 p r - 940 p r 10 5 5 5 4 5 3 2 5 2 3 + 35 p r - 9315 n p + 46575 n p r - 93150 n p r + 93150 n p r 5 4 5 5 4 6 4 5 - 46575 n p r + 9315 n r - 29250 n p + 128925 n p r 4 4 2 4 3 3 4 2 4 4 5 - 205875 n p r + 119250 n p r + 27000 n p r - 57375 n p r 4 6 3 7 3 6 3 5 2 + 17325 n r - 26490 n p + 68430 n p r + 52560 n p r 3 4 3 3 3 4 3 2 5 3 6 - 362100 n p r + 481350 n p r - 267210 n p r + 50820 n p r 3 7 2 8 2 7 2 6 2 + 2640 n r - 2000 n p - 63470 n p r + 324790 n p r 2 5 3 2 4 4 2 3 5 2 2 6 - 597020 n p r + 474700 n p r - 90950 n p r - 88130 n p r 2 7 2 8 9 8 7 2 + 46960 n p r - 4880 n r + 4330 n p - 42970 n p r + 108410 n p r 6 3 5 4 4 5 3 6 - 36430 n p r - 243865 n p r + 433745 n p r - 319480 n p r 2 7 8 9 10 9 + 111740 n p r - 16195 n p r + 715 n r - 240 p + 6730 p r 8 2 7 3 6 4 5 5 4 6 - 51770 p r + 174190 p r - 313940 p r + 327955 p r - 201005 p r 3 7 2 8 9 10 5 4 + 69220 p r - 11990 p r + 865 p r - 15 r + 28224 n p 5 3 5 2 2 5 3 5 4 - 112896 n p r + 169344 n p r - 112896 n p r + 28224 n r 4 5 4 4 4 3 2 4 2 3 + 89495 n p - 306355 n p r + 330470 n p r - 48230 n p r 4 4 4 5 3 6 3 5 - 117005 n p r + 51625 n r + 72900 n p - 79420 n p r 3 4 2 3 3 3 3 2 4 3 5 - 414160 n p r + 992840 n p r - 792860 n p r + 223540 n p r 3 6 2 7 2 6 2 5 2 - 2840 n r - 13830 n p + 315510 n p r - 1065660 n p r 2 4 3 2 3 4 2 2 5 2 6 + 1361940 n p r - 617310 n p r - 105330 n p r + 146880 n p r 2 7 8 7 6 2 - 22200 n r - 23260 n p + 158420 n p r - 238960 n p r 5 3 4 4 3 5 2 6 - 232520 n p r + 971620 n p r - 1024220 n p r + 477000 n p r 7 8 9 8 7 2 - 94320 n p r + 6240 n r + 2510 p - 45850 p r + 262610 p r 6 3 5 4 4 5 3 6 2 7 - 692410 p r + 980485 p r - 786161 p r + 353404 p r - 83316 p r 8 9 5 3 5 2 5 2 + 9039 p r - 311 r - 53532 n p + 160596 n p r - 160596 n p r 5 3 4 4 4 3 4 2 2 + 53532 n r - 169740 n p + 411300 n p r - 215460 n p r 4 3 4 4 3 5 3 4 - 124020 n p r + 97920 n r - 108880 n p - 134560 n p r 3 3 2 3 2 3 3 4 3 5 + 1091720 n p r - 1379000 n p r + 565480 n p r - 34760 n r 2 6 2 5 2 4 2 2 3 3 + 95700 n p - 900840 n p r + 2050260 n p r - 1641960 n p r 2 2 4 2 5 2 6 7 + 197220 n p r + 260400 n p r - 60780 n r + 76080 n p 6 5 2 4 3 3 4 - 341160 n p r + 122640 n p r + 1162440 n p r - 1983420 n p r 2 5 6 7 8 7 + 1268940 n p r - 336180 n p r + 30660 n r - 15060 p + 196560 p r 6 2 5 3 4 4 3 5 - 858540 p r + 1757960 p r - 1906840 p r + 1128788 p r 2 6 7 8 5 2 5 - 352904 p r + 52804 p r - 2768 r + 62239 n p - 124478 n p r 5 2 4 3 4 2 4 2 + 62239 n r + 192935 n p - 267610 n p r - 43585 n p r 4 3 3 4 3 3 3 2 2 + 118260 n r + 52590 n p + 561380 n p r - 1377290 n p r 3 3 3 4 2 5 2 4 + 860080 n p r - 96760 n r - 275230 n p + 1533920 n p r 2 3 2 2 2 3 2 4 2 5 - 2225770 n p r + 848480 n p r + 220820 n p r - 102220 n r 6 5 4 2 3 3 - 153675 n p + 371590 n p r + 604945 n p r - 2290440 n p r 2 4 5 6 7 6 + 2142070 n p r - 768500 n p r + 94010 n r + 57405 p - 555510 p r 5 2 4 3 3 4 2 5 + 1852325 p r - 2885560 p r + 2312950 p r - 959356 p r 6 7 5 5 4 2 + 191702 p r - 13956 r - 40695 n p + 40695 n r - 115630 n p 4 4 2 3 3 3 2 + 27785 n p r + 87845 n r + 85670 n p - 719530 n p r 3 2 3 3 2 4 2 3 + 775100 n p r - 141240 n r + 442440 n p - 1512750 n p r 2 2 2 2 3 2 4 5 + 1189830 n p r - 18120 n p r - 101400 n r + 180735 n p 4 3 2 2 3 4 - 18795 n p r - 1475160 n p r + 2268380 n p r - 1143250 n p r 5 6 5 4 2 3 3 + 188090 n r - 145350 p + 1052835 p r - 2641485 p r + 3030260 p r 2 4 5 6 5 4 - 1705600 p r + 453590 p r - 44250 r + 11500 n + 20975 n p 4 3 2 3 3 2 2 3 + 36525 n r - 148390 n p + 380680 n p r - 117290 n r - 406700 n p 2 2 2 2 2 3 4 + 774930 n p r - 203910 n p r - 49320 n r - 92970 n p 3 2 2 3 4 - 441520 n p r + 1437210 n p r - 1094080 n p r + 248860 n r 5 4 3 2 2 3 4 + 248275 p - 1334345 p r + 2447930 p r - 1968860 p r + 710910 p r 5 4 3 3 2 2 - 92410 r + 6500 n + 78410 n p - 52410 n r + 196720 n p 2 2 2 3 2 2 - 158210 n p r + 490 n r - 31010 n p + 486470 n p r - 644680 n p r 3 4 3 2 2 3 + 215220 n r - 284856 p + 1108414 p r - 1419386 p r + 731364 p r 4 3 2 2 2 - 129036 r - 9800 n - 40530 n p + 11130 n r + 64895 n p 2 3 2 2 - 210850 n p r + 116555 n r + 214893 p - 579784 p r + 474359 p r 3 2 2 - 119268 r + 3400 n - 28915 n p + 35715 n r - 102346 p + 175777 p r / 2 \ 2 |d | / - 70031 r + 4700 n + 28355 p - 23655 r - 3500) |--- A[n + 1](r, s)| / ( | 2 | / \dr / 2 2 2 2 2 2 2 2 2 (n p - 2 n p r + n r - 3 n p + 3 n r + 2 n p - 4 n p r + 2 n r 2 2 2 + 2 n - 6 n p + 6 n r + p - 2 p r + r + 4 n - 3 p + 3 r + 2) 3 2 2 5 7 5 6 5 5 2 (n + 3 n + 3 n + 1) %1 (r + s)) - (10 n p - 70 n p r + 210 n p r 5 4 3 5 3 4 5 2 5 5 6 5 7 - 350 n p r + 350 n p r - 210 n p r + 70 n p r - 10 n r 4 8 4 7 4 6 2 4 5 3 4 4 4 + 20 n p - 110 n p r + 210 n p r - 70 n p r - 350 n p r 4 3 5 4 2 6 4 7 4 8 3 9 + 630 n p r - 490 n p r + 190 n p r - 30 n r + 10 n p 3 8 3 7 2 3 6 3 3 5 4 3 4 5 - 10 n p r - 180 n p r + 700 n p r - 1120 n p r + 840 n p r 3 3 6 3 2 7 3 8 3 9 2 9 - 140 n p r - 220 n p r + 150 n p r - 30 n r + 30 n p r 2 8 2 2 7 3 2 6 4 2 5 5 - 150 n p r + 220 n p r + 140 n p r - 840 n p r 2 4 6 2 3 7 2 2 8 2 9 2 10 + 1120 n p r - 700 n p r + 180 n p r + 10 n p r - 10 n r 9 2 8 3 7 4 6 5 5 6 + 30 n p r - 190 n p r + 490 n p r - 630 n p r + 350 n p r 4 7 3 8 2 9 10 9 3 + 70 n p r - 210 n p r + 110 n p r - 20 n p r + 10 p r 8 4 7 5 6 6 5 7 4 8 3 9 - 70 p r + 210 p r - 350 p r + 350 p r - 210 p r + 70 p r 2 10 5 6 5 5 5 4 2 5 3 3 - 10 p r - 200 n p + 1200 n p r - 3000 n p r + 4000 n p r 5 2 4 5 5 5 6 4 7 4 6 - 3000 n p r + 1200 n p r - 200 n r - 400 n p + 1800 n p r 4 5 2 4 4 3 4 3 4 4 2 5 - 2400 n p r - 1000 n p r + 6000 n p r - 6600 n p r 4 6 4 7 3 8 3 7 3 6 2 + 3200 n p r - 600 n r - 170 n p - 240 n p r + 4440 n p r 3 5 3 3 4 4 3 3 5 3 2 6 - 12080 n p r + 14100 n p r - 6480 n p r - 1160 n p r 3 7 3 8 2 9 2 8 2 7 2 + 2160 n p r - 570 n r + 30 n p - 780 n p r + 2760 n p r 2 6 3 2 5 4 2 4 5 2 3 6 - 2000 n p r - 6060 n p r + 14520 n p r - 12920 n p r 2 2 7 2 8 2 9 9 8 2 + 5040 n p r - 450 n p r - 140 n r + 60 n p r - 1050 n p r 7 3 6 4 5 5 4 6 3 7 + 4640 n p r - 9120 n p r + 8520 n p r - 2260 n p r - 2400 n p r 2 8 9 10 9 2 8 3 7 4 + 2160 n p r - 580 n p r + 30 n r + 30 p r - 440 p r + 2040 p r 6 5 5 6 4 7 3 8 2 9 10 - 4680 p r + 6100 p r - 4680 p r + 2040 p r - 440 p r + 30 p r 5 5 5 4 5 3 2 5 2 3 + 1665 n p - 8325 n p r + 16650 n p r - 16650 n p r 5 4 5 5 4 6 4 5 4 4 2 + 8325 n p r - 1665 n r + 3300 n p - 11475 n p r + 7875 n p r 4 3 3 4 2 4 4 5 4 6 + 17250 n p r - 33750 n p r + 21825 n p r - 5025 n r 3 7 3 6 3 5 2 3 4 3 + 1000 n p + 6200 n p r - 41550 n p r + 79750 n p r 3 3 4 3 2 5 3 6 3 7 2 8 - 62500 n p r + 10500 n p r + 11050 n p r - 4450 n r - 630 n p 2 7 2 6 2 2 5 3 2 4 4 + 8040 n p r - 18840 n p r - 3870 n p r + 64650 n p r 2 3 5 2 2 6 2 7 2 8 9 - 89220 n p r + 49860 n p r - 9510 n p r - 480 n r + 30 n p 8 7 2 6 3 5 4 - 1530 n p r + 14160 n p r - 45600 n p r + 66465 n p r 4 5 3 6 2 7 8 9 - 40605 n p r - 2670 n p r + 15390 n p r - 6225 n p r + 585 n r 9 8 2 7 3 6 4 5 5 + 30 p r - 900 p r + 7120 p r - 23860 p r + 41925 p r 4 6 3 7 2 8 9 10 5 4 - 41705 p r + 23450 p r - 6870 p r + 835 p r - 25 r - 7475 n p 5 3 5 2 2 5 3 5 4 + 29900 n p r - 44850 n p r + 29900 n p r - 7475 n r 4 5 4 4 4 3 2 4 2 3 - 14425 n p + 34750 n p r + 5250 n p r - 80000 n p r 4 4 4 5 3 6 3 5 + 77375 n p r - 22950 n r - 1300 n p - 49900 n p r 3 4 2 3 3 3 3 2 4 3 5 + 194250 n p r - 252000 n p r + 109000 n p r + 18300 n p r 3 6 2 7 2 6 2 5 2 - 18350 n r + 5500 n p - 42400 n p r + 52350 n p r 2 4 3 2 3 4 2 2 5 2 6 + 107000 n p r - 296000 n p r + 243000 n p r - 71850 n p r 2 7 8 7 6 2 5 3 + 2400 n r - 670 n p + 16360 n p r - 99660 n p r + 234220 n p r 4 4 3 5 2 6 7 - 239275 n p r + 73020 n p r + 44490 n p r - 33240 n p r 8 9 8 7 2 6 3 5 4 + 4755 n r + 10 p - 760 p r + 11220 p r - 59400 p r + 147655 p r 4 5 3 6 2 7 8 9 - 195510 p r + 142510 p r - 54720 p r + 9525 p r - 530 r 5 3 5 2 5 2 5 3 4 4 + 19531 n p - 58593 n p r + 58593 n p r - 19531 n r + 35355 n p 4 3 4 2 2 4 3 4 4 - 43765 n p r - 80835 n p r + 151545 n p r - 62300 n r 3 5 3 4 3 3 2 3 2 3 - 11620 n p + 199520 n p r - 486570 n p r + 378790 n p r 3 4 3 5 2 6 2 5 - 37850 n p r - 42270 n r - 25700 n p + 119340 n p r 2 4 2 2 3 3 2 2 4 2 5 + 930 n p r - 487810 n p r + 649950 n p r - 282690 n p r 2 6 7 6 5 2 4 3 + 25980 n r + 6350 n p - 95850 n p r + 406890 n p r - 677530 n p r 3 4 2 5 6 7 8 + 433625 n p r - 195 n p r - 94165 n p r + 20875 n r - 230 p 7 6 2 5 3 4 4 3 5 + 8190 p r - 76590 p r + 288810 p r - 530395 p r + 511041 p r 2 6 7 8 5 2 5 - 255553 p r + 59563 p r - 4836 r - 29685 n p + 59370 n p r 5 2 4 3 4 2 4 2 - 29685 n r - 45845 n p - 10890 n p r + 159315 n p r 4 3 3 4 3 3 3 2 2 - 102580 n r + 62720 n p - 434260 n p r + 629610 n p r 3 3 3 4 2 5 2 4 - 207320 n p r - 50750 n r + 68340 n p - 153540 n p r 2 3 2 2 2 3 2 4 2 5 - 344310 n p r + 973920 n p r - 642450 n p r + 98040 n r 6 5 4 2 3 3 - 33300 n p + 336480 n p r - 994740 n p r + 1096780 n p r 2 4 5 6 7 6 - 335625 n p r - 122730 n p r + 53135 n r + 2260 p - 49120 p r 5 2 4 3 3 4 2 5 6 + 315600 p r - 857580 p r + 1131775 p r - 746190 p r + 228275 p r 7 5 5 4 2 4 - 25020 r + 24310 n p - 24310 n r + 21725 n p + 78100 n p r 4 2 3 3 3 2 3 2 - 99825 n r - 137890 n p + 500570 n p r - 344370 n p r 3 3 2 4 2 3 2 2 2 - 18310 n r - 98720 n p - 18790 n p r + 779040 n p r 2 3 2 4 5 4 - 863730 n p r + 202200 n r + 105515 n p - 725015 n p r 3 2 2 3 4 5 6 + 1431240 n p r - 911880 n p r + 24075 n p r + 76065 n r - 12400 p 5 4 2 3 3 2 4 5 + 179915 p r - 812295 p r + 1560140 p r - 1398075 p r + 564045 p r 6 5 4 4 3 2 - 81330 r - 8300 n + 11050 n p - 52550 n r + 150750 n p 3 3 2 2 3 2 2 - 257300 n p r + 23550 n r + 56710 n p + 282120 n p r 2 2 2 3 4 3 - 668070 n p r + 246240 n r - 206805 n p + 940640 n p r 2 2 3 4 5 4 - 1128840 n p r + 307180 n p r + 46325 n r + 41645 p - 415030 p r 3 2 2 3 4 5 4 + 1300380 p r - 1676660 p r + 915125 p r - 173760 r - 11500 n 3 3 2 2 2 2 2 - 73140 n p + 27140 n r + 25050 n p - 269520 n p r + 175470 n r 3 2 2 3 4 + 246055 n p - 688065 n p r + 418545 n p r - 22535 n r - 88195 p 3 2 2 3 4 3 + 598835 p r - 1242285 p r + 967705 p r - 247560 r + 8200 n 2 2 2 2 - 42620 n p + 67220 n r - 166825 n p + 248410 n p r - 56985 n r 3 2 2 3 2 + 116831 p - 517318 p r + 641523 p r - 232836 r + 10600 n + 56830 n p 2 2 - 35630 n r - 92535 p + 241900 p r - 138765 r - 7900 n + 39570 p / 3 \ |d | / 3 3 3 2 3 2 - 47470 r - 7100) |--- A[n + 1](r, s)| / ((n p - 3 n p r + 3 n p r | 3 | / \dr / 3 3 3 2 3 3 2 2 3 2 2 2 2 - n r - 6 n p + 12 n p r - 6 n r + 3 n p - 9 n p r + 9 n p r 2 3 3 3 2 2 2 2 2 3 - 3 n r + 11 n p - 11 n r - 18 n p + 36 n p r - 18 n r + 3 n p 2 2 3 3 2 2 2 - 9 n p r + 9 n p r - 3 n r - 6 n + 33 n p - 33 n r - 18 n p 2 3 2 2 3 2 + 36 n p r - 18 n r + p - 3 p r + 3 p r - r - 18 n + 33 n p - 33 n r 2 2 2 - 6 p + 12 p r - 6 r - 18 n + 11 p - 11 r - 6) (n + 2 n + 1) (r + s) ( 4 3 2 2 3 4 3 2 2 3 p - 4 p r + 6 p r - 4 p r + r - 10 p + 30 p r - 30 p r + 10 r 2 2 5 4 5 3 + 35 p - 70 p r + 35 r - 50 p + 50 r + 24)) + (5 n p - 20 n p r 5 2 2 5 3 5 4 4 5 4 3 2 + 30 n p r - 20 n p r + 5 n r + 5 n p - 50 n p r 4 2 3 4 4 4 5 3 5 3 4 2 + 100 n p r - 75 n p r + 20 n r + 20 n p r - 50 n p r 3 2 4 3 5 3 6 2 5 2 2 4 3 + 100 n p r - 100 n p r + 30 n r + 30 n p r - 100 n p r 2 3 4 2 6 2 7 5 3 4 4 + 100 n p r - 50 n p r + 20 n r + 20 n p r - 75 n p r 3 5 2 6 8 5 4 4 5 3 6 + 100 n p r - 50 n p r + 5 n r + 5 p r - 20 p r + 30 p r 2 7 8 5 3 5 2 5 2 5 3 - 20 p r + 5 p r - 60 n p + 180 n p r - 180 n p r + 60 n r 4 4 4 3 4 2 2 4 3 4 4 - 50 n p - 100 n p r + 600 n p r - 700 n p r + 250 n r 3 5 3 4 3 3 2 3 2 3 3 4 + 20 n p - 300 n p r + 400 n p r + 400 n p r - 900 n p r 3 5 2 5 2 4 2 2 3 3 2 2 4 + 380 n r + 60 n p r - 600 n p r + 1200 n p r - 600 n p r 2 5 2 6 5 2 4 3 3 4 - 300 n p r + 240 n r + 60 n p r - 500 n p r + 1100 n p r 2 5 6 7 5 3 4 4 3 5 - 900 n p r + 200 n p r + 40 n r + 20 p r - 150 p r + 340 p r 2 6 7 8 5 2 5 5 2 - 320 p r + 120 p r - 10 r + 255 n p - 510 n p r + 255 n r 4 3 4 2 4 2 4 3 3 4 + 125 n p + 900 n p r - 2175 n p r + 1150 n r - 250 n p 3 3 3 2 2 3 3 3 4 2 5 + 1500 n p r - 450 n p r - 2600 n p r + 1800 n r + 30 n p 2 4 2 3 2 2 2 3 2 4 2 5 - 900 n p r + 4050 n p r - 4500 n p r + 300 n p r + 1020 n r 5 4 2 3 3 2 4 5 + 60 n p r - 1050 n p r + 4100 n p r - 5325 n p r + 2250 n p r 6 5 2 4 3 3 4 2 5 6 - 35 n r + 30 p r - 400 p r + 1425 p r - 1920 p r + 1015 p r 7 5 5 4 2 4 4 2 - 150 r - 450 n p + 450 n r + 150 n p - 2550 n p r + 2400 n r 3 3 3 2 3 2 3 3 2 4 + 1100 n p - 2700 n p r - 2400 n p r + 4000 n r - 400 n p 2 3 2 2 2 2 3 2 4 5 + 4900 n p r - 11400 n p r + 5200 n p r + 1700 n r + 20 n p 4 3 2 2 3 4 5 - 900 n p r + 6700 n p r - 14300 n p r + 9750 n p r - 1270 n r 5 4 2 3 3 2 4 5 6 + 20 p r - 500 p r + 2900 p r - 5750 p r + 4250 p r - 920 r 5 4 4 3 2 3 3 2 + 274 n - 880 n p + 2250 n r - 1950 n p + 380 n p r + 4310 n r 2 3 2 2 2 2 2 3 4 + 1950 n p - 11700 n p r + 12270 n p r + 220 n r - 275 n p 3 2 2 3 4 5 4 + 5000 n p r - 19200 n p r + 20980 n p r - 5135 n r + 5 p - 300 p r 3 2 2 3 4 5 4 3 + 3100 p r - 9500 p r + 9995 p r - 3026 r + 770 n + 980 n p 3 2 2 2 2 2 3 + 2100 n r - 4200 n p + 11340 n p r - 2520 n r + 1400 n p 2 2 3 4 3 2 2 - 12600 n p r + 23940 n p r - 9660 n r - 70 p + 1680 p r - 8820 p r 3 4 3 2 2 2 + 13860 p r - 5880 r + 340 n + 3720 n p - 2700 n r - 3225 n p 2 3 2 2 3 + 13890 n p r - 9645 n r + 365 p - 4320 p r + 11265 p r - 6970 r 2 2 2 - 860 n + 3230 n p - 4950 n r - 870 p + 4970 p r - 4960 r - 1030 n / 4 \ |d | / 5 4 5 3 + 920 p - 1950 r - 326) |--- A[n + 1](r, s)| / ((n p - 4 n p r | 4 | / \dr / 5 2 2 5 3 5 4 5 3 5 2 5 2 + 6 n p r - 4 n p r + n r - 10 n p + 30 n p r - 30 n p r 5 3 4 4 4 3 4 2 2 4 3 4 4 + 10 n r + 5 n p - 20 n p r + 30 n p r - 20 n p r + 5 n r 5 2 5 5 2 4 3 4 2 4 2 + 35 n p - 70 n p r + 35 n r - 50 n p + 150 n p r - 150 n p r 4 3 3 4 3 3 3 2 2 3 3 3 4 + 50 n r + 10 n p - 40 n p r + 60 n p r - 40 n p r + 10 n r 5 5 4 2 4 4 2 3 3 - 50 n p + 50 n r + 175 n p - 350 n p r + 175 n r - 100 n p 3 2 3 2 3 3 2 4 2 3 + 300 n p r - 300 n p r + 100 n r + 10 n p - 40 n p r 2 2 2 2 3 2 4 5 4 4 + 60 n p r - 40 n p r + 10 n r + 24 n - 250 n p + 250 n r 3 2 3 3 2 2 3 2 2 + 350 n p - 700 n p r + 350 n r - 100 n p + 300 n p r 2 2 2 3 4 3 2 2 3 - 300 n p r + 100 n r + 5 n p - 20 n p r + 30 n p r - 20 n p r 4 4 3 3 2 2 2 + 5 n r + 120 n - 500 n p + 500 n r + 350 n p - 700 n p r 2 2 3 2 2 3 4 3 + 350 n r - 50 n p + 150 n p r - 150 n p r + 50 n r + p - 4 p r 2 2 3 4 3 2 2 2 + 6 p r - 4 p r + r + 240 n - 500 n p + 500 n r + 175 n p 2 3 2 2 3 2 - 350 n p r + 175 n r - 10 p + 30 p r - 30 p r + 10 r + 240 n 2 2 - 250 n p + 250 n r + 35 p - 70 p r + 35 r + 120 n - 50 p + 50 r + 24) 5 4 3 2 2 3 4 5 4 (r + s)) - (n + 5 n r + 10 n r + 10 n r + 5 n r + r + 5 n 3 2 2 3 4 3 2 2 3 + 20 n r + 30 n r + 20 n r + 5 r + 10 n + 30 n r + 30 n r + 10 r / 5 \ 2 2 |d | / + 10 n + 20 n r + 10 r + 5 n + 5 r + 1) |--- A[n + 1](r, s)| / ( | 5 | / \dr / 5 4 3 2 (n + 5 n + 10 n + 10 n + 5 n + 1) (r + s)) = 0 3 2 2 3 2 2 %1 := p - 3 p r + 3 p r - r - 6 p + 12 p r - 6 r + 11 p - 11 r - 6 3 2 2 2 2 3 2 2 3 (n + 3 n q - 3 n s + 3 n q - 6 n q s + 3 n s + q - 3 q s + 3 q s - s 2 2 2 - 6 n - 12 n q + 12 n s - 6 q + 12 q s - 6 s + 11 n + 11 q - 11 s - 6) / 3 5 4 4 3 2 A[n](r, s) / (n + q - s) - (4 n + 20 n q - 20 n s + 40 n q / 3 3 2 2 3 2 2 2 2 2 3 - 80 n q s + 40 n s + 40 n q - 120 n q s + 120 n q s - 40 n s 4 3 2 2 3 4 5 4 + 20 n q - 80 n q s + 120 n q s - 80 n q s + 20 n s + 4 q - 20 q s 3 2 2 3 4 5 4 3 3 + 40 q s - 40 q s + 20 q s - 4 s - 26 n - 104 n q + 104 n s 2 2 2 2 2 3 2 2 - 156 n q + 312 n q s - 156 n s - 104 n q + 312 n q s - 312 n q s 3 4 3 2 2 3 4 3 + 104 n s - 26 q + 104 q s - 156 q s + 104 q s - 26 s + 58 n 2 2 2 2 3 2 + 174 n q - 174 n s + 174 n q - 348 n q s + 174 n s + 58 q - 174 q s 2 3 2 2 2 + 174 q s - 58 s - 57 n - 114 n q + 114 n s - 57 q + 114 q s - 57 s /d \ / + 29 n + 29 q - 29 s - 6) |-- A[n](r, s)| / ((n + q - s) \ds / / 2 2 2 2 5 4 (n + 2 n q - 2 n s + q - 2 q s + s - n - q + s) ) + (6 n + 30 n q 4 3 2 3 3 2 2 3 2 2 - 30 n s + 60 n q - 120 n q s + 60 n s + 60 n q - 180 n q s 2 2 2 3 4 3 2 2 3 + 180 n q s - 60 n s + 30 n q - 120 n q s + 180 n q s - 120 n q s 4 5 4 3 2 2 3 4 5 4 + 30 n s + 6 q - 30 q s + 60 q s - 60 q s + 30 q s - 6 s - 42 n 3 3 2 2 2 2 2 3 - 168 n q + 168 n s - 252 n q + 504 n q s - 252 n s - 168 n q 2 2 3 4 3 2 2 + 504 n q s - 504 n q s + 168 n s - 42 q + 168 q s - 252 q s 3 4 3 2 2 2 + 168 q s - 42 s + 105 n + 315 n q - 315 n s + 315 n q - 630 n q s 2 3 2 2 3 2 + 315 n s + 105 q - 315 q s + 315 q s - 105 s - 117 n - 234 n q 2 2 + 234 n s - 117 q + 234 q s - 117 s + 58 n + 58 q - 58 s - 12) / 2 \ |d | / 3 2 2 2 2 |--- A[n](r, s)| / ((n + 3 n q - 3 n s + 3 n q - 6 n q s + 3 n s | 2 | / \ds / 3 2 2 3 2 2 2 + q - 3 q s + 3 q s - s - 3 n - 6 n q + 6 n s - 3 q + 6 q s - 3 s 2 2 2 + 2 n + 2 q - 2 s) (n + 2 n q - 2 n s + q - 2 q s + s - n - q + s)) - 2 3 2 2 2 2 3 2 (2 n + 6 n q - 6 n s + 6 n q - 12 n q s + 6 n s + 2 q - 6 q s 2 3 2 2 2 + 6 q s - 2 s - 9 n - 18 n q + 18 n s - 9 q + 18 q s - 9 s + 11 n / 3 \ |d | / 3 2 2 2 + 11 q - 11 s - 3) |--- A[n](r, s)| / (n + 3 n q - 3 n s + 3 n q | 3 | / \ds / 2 3 2 2 3 2 - 6 n q s + 3 n s + q - 3 q s + 3 q s - s - 3 n - 6 n q + 6 n s / 4 \ 2 2 |d | 4 3 - 3 q + 6 q s - 3 s + 2 n + 2 q - 2 s) + |--- A[n](r, s)| - (n + 4 n q | 4 | \ds / 3 2 2 2 2 2 3 2 2 - 4 n s + 6 n q - 12 n q s + 6 n s + 4 n q - 12 n q s + 12 n q s 3 4 3 2 2 3 4 3 2 2 - 4 n s + q - 4 q s + 6 q s - 4 q s + s - 6 n - 18 n q + 18 n s 2 2 3 2 2 3 2 - 18 n q + 36 n q s - 18 n s - 6 q + 18 q s - 18 q s + 6 s + 11 n 2 2 5 + 22 n q - 22 n s + 11 q - 22 q s + 11 s - 6 n - 6 q + 6 s) q / A[n + 1](r, s) / ( / 2 2 2 2 (n + 2 n q - 2 n s + q - 2 q s + s + 2 n + 2 q - 2 s + 1) 5 4 3 2 8 4 (n + 5 n + 10 n + 10 n + 5 n + 1) (q + n - s + 1)) - (5 n q 7 5 7 4 6 6 6 5 6 4 2 + 35 n q - 40 n q s + 105 n q - 245 n q s + 140 n q s 5 7 5 6 5 5 2 5 4 3 4 8 + 175 n q - 630 n q s + 735 n q s - 280 n q s + 175 n q 4 7 4 6 2 4 5 3 4 4 4 3 9 - 875 n q s + 1575 n q s - 1225 n q s + 350 n q s + 105 n q 3 8 3 7 2 3 6 3 3 5 4 - 700 n q s + 1750 n q s - 2100 n q s + 1225 n q s 3 4 5 2 10 2 9 2 8 2 2 7 3 - 280 n q s + 35 n q - 315 n q s + 1050 n q s - 1750 n q s 2 6 4 2 5 5 2 4 6 11 10 + 1575 n q s - 735 n q s + 140 n q s + 5 n q - 70 n q s 9 2 8 3 7 4 6 5 5 6 + 315 n q s - 700 n q s + 875 n q s - 630 n q s + 245 n q s 4 7 11 10 2 9 3 8 4 7 5 - 40 n q s - 5 q s + 35 q s - 105 q s + 175 q s - 175 q s 6 6 5 7 4 8 8 3 7 4 7 3 + 105 q s - 35 q s + 5 q s - 10 n q - 85 n q + 80 n q s 6 5 6 4 6 3 2 5 6 5 5 - 295 n q + 595 n q s - 280 n q s - 545 n q + 1770 n q s 5 4 2 5 3 3 4 7 4 6 4 5 2 - 1785 n q s + 560 n q s - 575 n q + 2725 n q s - 4425 n q s 4 4 3 4 3 4 3 8 3 7 3 6 2 + 2975 n q s - 700 n q s - 335 n q + 2300 n q s - 5450 n q s 3 5 3 3 4 4 3 3 5 2 9 2 8 + 5900 n q s - 2975 n q s + 560 n q s - 85 n q + 1005 n q s 2 7 2 2 6 3 2 5 4 2 4 5 - 3450 n q s + 5450 n q s - 4425 n q s + 1785 n q s 2 3 6 10 9 8 2 7 3 - 280 n q s + 5 n q + 170 n q s - 1005 n q s + 2300 n q s 6 4 5 5 4 6 3 7 11 10 - 2725 n q s + 1770 n q s - 595 n q s + 80 n q s + 5 q - 5 q s 9 2 8 3 7 4 6 5 5 6 4 7 - 85 q s + 335 q s - 575 q s + 545 q s - 295 q s + 85 q s 3 8 8 2 7 3 7 2 6 4 6 3 - 10 q s + 10 n q + 90 n q - 80 n q s + 305 n q - 630 n q s 6 2 2 5 5 5 4 5 3 2 5 2 3 + 280 n q s + 495 n q - 1830 n q s + 1890 n q s - 560 n q s 4 6 4 5 4 4 2 4 3 3 4 2 4 + 350 n q - 2475 n q s + 4575 n q s - 3150 n q s + 700 n q s 3 7 3 6 3 5 2 3 4 3 3 3 4 - 40 n q - 1400 n q s + 4950 n q s - 6100 n q s + 3150 n q s 3 2 5 2 8 2 7 2 6 2 2 5 3 - 560 n q s - 235 n q + 120 n q s + 2100 n q s - 4950 n q s 2 4 4 2 3 5 2 2 6 9 8 + 4575 n q s - 1890 n q s + 280 n q s - 145 n q + 470 n q s 7 2 6 3 5 4 4 5 3 6 - 120 n q s - 1400 n q s + 2475 n q s - 1830 n q s + 630 n q s 2 7 10 9 8 2 7 3 6 4 - 80 n q s - 30 q + 145 q s - 235 q s + 40 q s + 350 q s 5 5 4 6 3 7 2 8 8 7 2 - 495 q s + 305 q s - 90 q s + 10 q s - 5 n q - 50 n q 7 6 3 6 2 6 2 5 4 + 40 n q s - 120 n q + 350 n q s - 140 n q s + 45 n q 5 3 5 2 2 5 3 4 5 4 4 + 720 n q s - 1050 n q s + 280 n q s + 600 n q - 225 n q s 4 3 2 4 2 3 4 4 3 6 3 5 - 1800 n q s + 1750 n q s - 350 n q s + 1020 n q - 2400 n q s 3 4 2 3 3 3 3 2 4 3 5 2 7 + 450 n q s + 2400 n q s - 1750 n q s + 280 n q s + 800 n q 2 6 2 5 2 2 4 3 2 3 4 - 3060 n q s + 3600 n q s - 450 n q s - 1800 n q s 2 2 5 2 6 8 7 6 2 + 1050 n q s - 140 n q s + 305 n q - 1600 n q s + 3060 n q s 5 3 4 4 3 5 2 6 7 - 2400 n q s + 225 n q s + 720 n q s - 350 n q s + 40 n q s 9 8 7 2 6 3 5 4 4 5 + 45 q - 305 q s + 800 q s - 1020 q s + 600 q s - 45 q s 3 6 2 7 8 8 7 7 6 2 - 120 q s + 50 q s - 5 q s + n + 13 n q - 8 n s - 27 n q 6 6 2 5 3 5 2 5 2 5 3 - 91 n q s + 28 n s - 369 n q + 162 n q s + 273 n q s - 56 n s 4 4 4 3 4 2 2 4 3 4 4 - 930 n q + 1845 n q s - 405 n q s - 455 n q s + 70 n s 3 5 3 4 3 3 2 3 2 3 3 4 - 990 n q + 3720 n q s - 3690 n q s + 540 n q s + 455 n q s 3 5 2 6 2 5 2 4 2 2 3 3 - 56 n s - 430 n q + 2970 n q s - 5580 n q s + 3690 n q s 2 2 4 2 5 2 6 7 6 - 405 n q s - 273 n q s + 28 n s - 10 n q + 860 n q s 5 2 4 3 3 4 2 5 6 - 2970 n q s + 3720 n q s - 1845 n q s + 162 n q s + 91 n q s 7 8 7 6 2 5 3 4 4 3 5 - 8 n s + 30 q + 10 q s - 430 q s + 990 q s - 930 q s + 369 q s 2 6 7 8 7 6 6 5 2 5 - 27 q s - 13 q s + s - n + 38 n q + 7 n s + 239 n q - 228 n q s 5 2 4 3 4 2 4 2 4 3 3 4 - 21 n s + 340 n q - 1195 n q s + 570 n q s + 35 n s - 130 n q 3 3 3 2 2 3 3 3 4 2 5 - 1360 n q s + 2390 n q s - 760 n q s - 35 n s - 620 n q 2 4 2 3 2 2 2 3 2 4 2 5 + 390 n q s + 2040 n q s - 2390 n q s + 570 n q s + 21 n s 6 5 4 2 3 3 2 4 - 450 n q + 1240 n q s - 390 n q s - 1360 n q s + 1195 n q s 5 6 7 6 5 2 4 3 - 228 n q s - 7 n s - 100 q + 450 q s - 620 q s + 130 q s 3 4 2 5 6 7 6 5 5 + 340 q s - 239 q s + 38 q s + s - 9 n - 49 n q + 54 n s 4 2 4 4 2 3 3 3 2 + 140 n q + 245 n q s - 135 n s + 660 n q - 560 n q s 3 2 3 3 2 4 2 3 2 2 2 - 490 n q s + 180 n s + 730 n q - 1980 n q s + 840 n q s 2 3 2 4 5 4 3 2 + 490 n q s - 135 n s + 250 n q - 1460 n q s + 1980 n q s 2 3 4 5 5 4 2 3 3 - 560 n q s - 245 n q s + 54 n s - 250 q s + 730 q s - 660 q s 2 4 5 6 5 4 4 3 2 + 140 q s + 49 q s - 9 s - n - 130 n q + 5 n s - 300 n q 3 3 2 2 3 2 2 2 2 2 3 + 520 n q s - 10 n s - 20 n q + 900 n q s - 780 n q s + 10 n s 4 3 2 2 3 4 5 + 250 n q + 40 n q s - 900 n q s + 520 n q s - 5 n s + 105 q 4 3 2 2 3 4 5 4 3 - 250 q s - 20 q s + 300 q s - 130 q s + s + 25 n - 5 n q 3 2 2 2 2 2 3 2 - 100 n s - 275 n q + 15 n q s + 150 n s - 245 n q + 550 n q s 2 3 4 3 2 2 3 4 - 15 n q s - 100 n s - 30 q + 245 q s - 275 q s + 5 q s + 25 s 3 2 2 2 2 3 + 21 n + 118 n q - 63 n s - 17 n q - 236 n q s + 63 n s - 54 q 2 2 3 2 2 + 17 q s + 118 q s - 21 s - 11 n + 73 n q + 22 n s + 24 q - 73 q s 2 /d \ / 6 5 - 11 s - 19 n + 11 q + 19 s - 6) |-- A[n + 1](r, s)| / ((n + n q \ds / / 5 5 4 4 4 3 3 3 - n s + 6 n + 5 n q - 5 n s + 15 n + 10 n q - 10 n s + 20 n 2 2 2 + 10 n q - 10 n s + 15 n + 5 n q - 5 n s + 6 n + q - s + 1) 2 4 3 3 2 2 2 2 2 (q + n - s + 1) (n + 4 n q - 4 n s + 6 n q - 12 n q s + 6 n s 3 2 2 3 4 3 2 2 3 + 4 n q - 12 n q s + 12 n q s - 4 n s + q - 4 q s + 6 q s - 4 q s 4 3 2 2 2 2 3 2 + s + 2 n + 6 n q - 6 n s + 6 n q - 12 n q s + 6 n s + 2 q - 6 q s 2 3 2 2 2 + 6 q s - 2 s + n + 2 n q - 2 n s + q - 2 q s + s ) (n + q - s)) - 2 7 3 6 4 6 3 5 5 (n - s + 1) (-s - 3 + q + n) (10 n q + 70 n q - 70 n q s + 210 n q 5 4 5 3 2 4 6 4 5 4 4 2 - 420 n q s + 210 n q s + 350 n q - 1050 n q s + 1050 n q s 4 3 3 3 7 3 6 3 5 2 3 4 3 - 350 n q s + 350 n q - 1400 n q s + 2100 n q s - 1400 n q s 3 3 4 2 8 2 7 2 6 2 2 5 3 + 350 n q s + 210 n q - 1050 n q s + 2100 n q s - 2100 n q s 2 4 4 2 3 5 9 8 7 2 + 1050 n q s - 210 n q s + 70 n q - 420 n q s + 1050 n q s 6 3 5 4 4 5 3 6 10 - 1400 n q s + 1050 n q s - 420 n q s + 70 n q s + 10 q 9 8 2 7 3 6 4 5 5 4 6 - 70 q s + 210 q s - 350 q s + 350 q s - 210 q s + 70 q s 3 7 7 2 6 3 6 2 5 4 5 3 - 10 q s - 30 n q - 230 n q + 210 n q s - 750 n q + 1380 n q s 5 2 2 4 5 4 4 4 3 2 4 2 3 - 630 n q s - 1350 n q + 3750 n q s - 3450 n q s + 1050 n q s 3 6 3 5 3 4 2 3 3 3 - 1450 n q + 5400 n q s - 7500 n q s + 4600 n q s 3 2 4 2 7 2 6 2 5 2 2 4 3 - 1050 n q s - 930 n q + 4350 n q s - 8100 n q s + 7500 n q s 2 3 4 2 2 5 8 7 6 2 - 3450 n q s + 630 n q s - 330 n q + 1860 n q s - 4350 n q s 5 3 4 4 3 5 2 6 9 + 5400 n q s - 3750 n q s + 1380 n q s - 210 n q s - 50 q 8 7 2 6 3 5 4 4 5 3 6 + 330 q s - 930 q s + 1450 q s - 1350 q s + 750 q s - 230 q s 2 7 7 6 2 6 5 3 5 2 + 30 q s + 35 n q + 275 n q - 245 n q s + 910 n q - 1650 n q s 5 2 4 4 4 3 4 2 2 4 3 + 735 n q s + 1650 n q - 4550 n q s + 4125 n q s - 1225 n q s 3 5 3 4 3 3 2 3 2 3 3 4 + 1775 n q - 6600 n q s + 9100 n q s - 5500 n q s + 1225 n q s 2 6 2 5 2 4 2 2 3 3 + 1135 n q - 5325 n q s + 9900 n q s - 9100 n q s 2 2 4 2 5 7 6 5 2 + 4125 n q s - 735 n q s + 400 n q - 2270 n q s + 5325 n q s 4 3 3 4 2 5 6 8 - 6600 n q s + 4550 n q s - 1650 n q s + 245 n q s + 60 q 7 6 2 5 3 4 4 3 5 2 6 - 400 q s + 1135 q s - 1775 q s + 1650 q s - 910 q s + 275 q s 7 7 6 6 5 2 5 - 35 q s - 15 n - 115 n q + 105 n s - 300 n q + 690 n q s 5 2 4 3 4 2 4 2 4 3 - 315 n s - 290 n q + 1500 n q s - 1725 n q s + 525 n s 3 4 3 3 3 2 2 3 3 3 4 + 65 n q + 1160 n q s - 3000 n q s + 2300 n q s - 525 n s 2 5 2 4 2 3 2 2 2 3 2 4 + 345 n q - 195 n q s - 1740 n q s + 3000 n q s - 1725 n q s 2 5 6 5 4 2 3 3 + 315 n s + 250 n q - 690 n q s + 195 n q s + 1160 n q s 2 4 5 6 7 6 5 2 - 1500 n q s + 690 n q s - 105 n s + 60 q - 250 q s + 345 q s 4 3 3 4 2 5 6 7 6 5 - 65 q s - 290 q s + 300 q s - 115 q s + 15 s - 4 n - 137 n q 5 4 2 4 4 2 3 3 3 2 + 24 n s - 647 n q + 685 n q s - 60 n s - 1294 n q + 2588 n q s 3 2 3 3 2 4 2 3 2 2 2 - 1370 n q s + 80 n s - 1310 n q + 3882 n q s - 3882 n q s 2 3 2 4 5 4 3 2 + 1370 n q s - 60 n s - 665 n q + 2620 n q s - 3882 n q s 2 3 4 5 6 5 4 2 + 2588 n q s - 685 n q s + 24 n s - 135 q + 665 q s - 1310 q s 3 3 2 4 5 6 5 4 4 + 1294 q s - 647 q s + 137 q s - 4 s + 51 n + 225 n q - 255 n s 3 2 3 3 2 2 3 2 2 + 362 n q - 900 n q s + 510 n s + 238 n q - 1086 n q s 2 2 2 3 4 3 2 2 + 1350 n q s - 510 n s + 35 n q - 476 n q s + 1086 n q s 3 4 5 4 3 2 2 3 - 900 n q s + 255 n s - 15 q - 35 q s + 238 q s - 362 q s 4 5 4 3 3 2 2 2 + 225 q s - 51 s + 38 n + 193 n q - 152 n s + 373 n q - 579 n q s 2 2 3 2 2 3 4 + 228 n s + 318 n q - 746 n q s + 579 n q s - 152 n s + 100 q 3 2 2 3 4 3 2 2 - 318 q s + 373 q s - 193 q s + 38 s - 9 n - 41 n q + 27 n s 2 2 3 2 2 3 - 48 n q + 82 n q s - 27 n s - 14 q + 48 q s - 41 q s + 9 s - 11 n q / 2 \ 2 |d | / - 17 q + 11 q s + 5 n + 11 q - 5 s - 2) |--- A[n + 1](r, s)| / ( | 2 | / \ds / 5 3 4 2 10 2 (n + 1) (n + q - s) (q + n - s + 1) (n + q - s - 1) ) - (10 n q 9 3 9 2 8 4 8 3 8 2 2 + 70 n q - 100 n q s + 210 n q - 630 n q s + 450 n q s 7 5 7 4 7 3 2 7 2 3 6 6 + 350 n q - 1680 n q s + 2520 n q s - 1200 n q s + 350 n q 6 5 6 4 2 6 3 3 6 2 4 5 7 - 2450 n q s + 5880 n q s - 5880 n q s + 2100 n q s + 210 n q 5 6 5 5 2 5 4 3 5 3 4 - 2100 n q s + 7350 n q s - 11760 n q s + 8820 n q s 5 2 5 4 8 4 7 4 6 2 4 5 3 - 2520 n q s + 70 n q - 1050 n q s + 5250 n q s - 12250 n q s 4 4 4 4 3 5 4 2 6 3 9 3 8 + 14700 n q s - 8820 n q s + 2100 n q s + 10 n q - 280 n q s 3 7 2 3 6 3 3 5 4 3 4 5 + 2100 n q s - 7000 n q s + 12250 n q s - 11760 n q s 3 3 6 3 2 7 2 9 2 8 2 + 5880 n q s - 1200 n q s - 30 n q s + 420 n q s 2 7 3 2 6 4 2 5 5 2 4 6 - 2100 n q s + 5250 n q s - 7350 n q s + 5880 n q s 2 3 7 2 2 8 9 2 8 3 7 4 - 2520 n q s + 450 n q s + 30 n q s - 280 n q s + 1050 n q s 6 5 5 6 4 7 3 8 2 9 - 2100 n q s + 2450 n q s - 1680 n q s + 630 n q s - 100 n q s 9 3 8 4 7 5 6 6 5 7 4 8 - 10 q s + 70 q s - 210 q s + 350 q s - 350 q s + 210 q s 3 9 2 10 10 9 2 9 8 3 - 70 q s + 10 q s - 30 n q - 240 n q + 300 n q s - 780 n q 8 2 8 2 7 4 7 3 7 2 2 + 2160 n q s - 1350 n q s - 1320 n q + 6240 n q s - 8640 n q s 7 3 6 5 6 4 6 3 2 + 3600 n q s - 1200 n q + 9240 n q s - 21840 n q s 6 2 3 6 4 5 6 5 5 + 20160 n q s - 6300 n q s - 480 n q + 7200 n q s 5 4 2 5 3 3 5 2 4 5 5 - 27720 n q s + 43680 n q s - 30240 n q s + 7560 n q s 4 7 4 6 4 5 2 4 4 3 + 60 n q + 2400 n q s - 18000 n q s + 46200 n q s 4 3 4 4 2 5 4 6 3 8 3 7 - 54600 n q s + 30240 n q s - 6300 n q s + 120 n q - 240 n q s 3 6 2 3 5 3 3 4 4 3 3 5 - 4800 n q s + 24000 n q s - 46200 n q s + 43680 n q s 3 2 6 3 7 2 9 2 8 2 7 2 - 20160 n q s + 3600 n q s + 30 n q - 360 n q s + 360 n q s 2 6 3 2 5 4 2 4 5 2 3 6 + 4800 n q s - 18000 n q s + 27720 n q s - 21840 n q s 2 2 7 2 8 9 8 2 7 3 + 8640 n q s - 1350 n q s - 60 n q s + 360 n q s - 240 n q s 6 4 5 5 4 6 3 7 2 8 - 2400 n q s + 7200 n q s - 9240 n q s + 6240 n q s - 2160 n q s 9 9 2 8 3 7 4 6 5 5 6 + 300 n q s + 30 q s - 120 q s + 60 q s + 480 q s - 1200 q s 4 7 3 8 2 9 10 10 9 + 1320 q s - 780 q s + 240 q s - 30 q s + 25 n + 235 n q 9 8 2 8 8 2 7 3 - 250 n s + 750 n q - 2115 n q s + 1125 n s + 890 n q 7 2 7 2 7 3 6 4 6 3 - 6000 n q s + 8460 n q s - 3000 n s - 295 n q - 6230 n q s 6 2 2 6 3 6 4 5 5 5 4 + 21000 n q s - 19740 n q s + 5250 n s - 1875 n q + 1770 n q s 5 3 2 5 2 3 5 4 5 5 + 18690 n q s - 42000 n q s + 29610 n q s - 6300 n s 4 6 4 5 4 4 2 4 3 3 - 1940 n q + 9375 n q s - 4425 n q s - 31150 n q s 4 2 4 4 5 4 6 3 7 3 6 + 52500 n q s - 29610 n q s + 5250 n s - 800 n q + 7760 n q s 3 5 2 3 4 3 3 3 4 3 2 5 - 18750 n q s + 5900 n q s + 31150 n q s - 42000 n q s 3 6 3 7 2 8 2 7 2 6 2 + 19740 n q s - 3000 n s - 60 n q + 2400 n q s - 11640 n q s 2 5 3 2 4 4 2 3 5 2 2 6 + 18750 n q s - 4425 n q s - 18690 n q s + 21000 n q s 2 7 2 8 9 8 7 2 - 8460 n q s + 1125 n s + 30 n q + 120 n q s - 2400 n q s 6 3 5 4 4 5 3 6 2 7 + 7760 n q s - 9375 n q s + 1770 n q s + 6230 n q s - 6000 n q s 8 9 9 8 2 7 3 6 4 + 2115 n q s - 250 n s - 30 q s - 60 q s + 800 q s - 1940 q s 5 5 4 6 3 7 2 8 9 10 + 1875 q s - 295 q s - 890 q s + 750 q s - 235 q s + 25 s 9 8 8 7 2 7 7 2 - 30 n + 105 n q + 270 n s + 1440 n q - 840 n q s - 1080 n s 6 3 6 2 6 2 6 3 5 4 + 4350 n q - 10080 n q s + 2940 n q s + 2520 n s + 5910 n q 5 3 5 2 2 5 3 5 4 4 5 - 26100 n q s + 30240 n q s - 5880 n q s - 3780 n s + 3595 n q 4 4 4 3 2 4 2 3 4 4 - 29550 n q s + 65250 n q s - 50400 n q s + 7350 n q s 4 5 3 6 3 5 3 4 2 3 3 3 + 3780 n s + 280 n q - 14380 n q s + 59100 n q s - 87000 n q s 3 2 4 3 5 3 6 2 7 2 6 + 50400 n q s - 5880 n q s - 2520 n s - 660 n q - 840 n q s 2 5 2 2 4 3 2 3 4 2 2 5 + 21570 n q s - 59100 n q s + 65250 n q s - 30240 n q s 2 6 2 7 8 7 6 2 + 2940 n q s + 1080 n s - 200 n q + 1320 n q s + 840 n q s 5 3 4 4 3 5 2 6 - 14380 n q s + 29550 n q s - 26100 n q s + 10080 n q s 7 8 9 8 7 2 6 3 - 840 n q s - 270 n s + 10 q + 200 q s - 660 q s - 280 q s 5 4 4 5 3 6 2 7 8 9 + 3595 q s - 5910 q s + 4350 q s - 1440 q s + 105 q s + 30 s 8 7 7 6 2 6 6 2 - 204 n - 1397 n q + 1632 n s - 3167 n q + 9779 n q s - 5712 n s 5 3 5 2 5 2 5 3 4 4 - 2079 n q + 19002 n q s - 29337 n q s + 11424 n s + 2395 n q 4 3 4 2 2 4 3 4 4 + 10395 n q s - 47505 n q s + 48895 n q s - 14280 n s 3 5 3 4 3 3 2 3 2 3 + 4570 n q - 9580 n q s - 20790 n q s + 63340 n q s 3 4 3 5 2 6 2 5 - 48895 n q s + 11424 n s + 2430 n q - 13710 n q s 2 4 2 2 3 3 2 2 4 2 5 + 14370 n q s + 20790 n q s - 47505 n q s + 29337 n q s 2 6 7 6 5 2 4 3 - 5712 n s + 270 n q - 4860 n q s + 13710 n q s - 9580 n q s 3 4 2 5 6 7 8 - 10395 n q s + 19002 n q s - 9779 n q s + 1632 n s - 90 q 7 6 2 5 3 4 4 3 5 - 270 q s + 2430 q s - 4570 q s + 2395 q s + 2079 q s 2 6 7 8 7 6 6 - 3167 q s + 1397 q s - 204 s + 36 n - 873 n q - 252 n s 5 2 5 5 2 4 3 4 2 - 4674 n q + 5238 n q s + 756 n s - 8525 n q + 23370 n q s 4 2 4 3 3 4 3 3 3 2 2 - 13095 n q s - 1260 n s - 6500 n q + 34100 n q s - 46740 n q s 3 3 3 4 2 5 2 4 2 3 2 + 17460 n q s + 1260 n s - 1260 n q + 19500 n q s - 51150 n q s 2 2 3 2 4 2 5 6 5 + 46740 n q s - 13095 n q s - 756 n s + 760 n q + 2520 n q s 4 2 3 3 2 4 5 6 - 19500 n q s + 34100 n q s - 23370 n q s + 5238 n q s + 252 n s 7 6 5 2 4 3 3 4 2 5 + 280 q - 760 q s - 1260 q s + 6500 q s - 8525 q s + 4674 q s 6 7 6 5 5 4 2 - 873 q s - 36 s + 522 n + 2277 n q - 3132 n s + 2475 n q 4 4 2 3 3 3 2 3 2 - 11385 n q s + 7830 n s - 1380 n q - 9900 n q s + 22770 n q s 3 3 2 4 2 3 2 2 2 2 3 - 10440 n s - 3945 n q + 4140 n q s + 14850 n q s - 22770 n q s 2 4 5 4 3 2 2 3 + 7830 n s - 2125 n q + 7890 n q s - 4140 n q s - 9900 n q s 4 5 6 5 4 2 3 3 + 11385 n q s - 3132 n s - 280 q + 2125 q s - 3945 q s + 1380 q s 2 4 5 6 5 4 4 + 2475 q s - 2277 q s + 522 s + 168 n + 1985 n q - 840 n s 3 2 3 3 2 2 3 2 2 + 4820 n q - 7940 n q s + 1680 n s + 4020 n q - 14460 n q s 2 2 2 3 4 3 2 2 + 11910 n q s - 1680 n s + 790 n q - 8040 n q s + 14460 n q s 3 4 5 4 3 2 2 3 - 7940 n q s + 840 n s - 215 q - 790 q s + 4020 q s - 4820 q s 4 5 4 3 3 2 2 + 1985 q s - 168 s - 480 n - 855 n q + 1920 n s + 525 n q 2 2 2 3 2 2 + 2565 n q s - 2880 n s + 1475 n q - 1050 n q s - 2565 n q s 3 4 3 2 2 3 4 3 + 1920 n s + 515 q - 1475 q s + 525 q s + 855 q s - 480 s - 324 n 2 2 2 2 3 - 1077 n q + 972 n s - 962 n q + 2154 n q s - 972 n s - 89 q 2 2 3 2 2 + 962 q s - 1077 q s + 324 s + 21 n - 68 n q - 42 n s - 209 q / 3 \ 2 |d | / 12 + 68 q s + 21 s + 22 n + 82 q - 22 s - 12) |--- A[n + 1](r, s)| / ((n | 3 | / \ds / 11 11 10 2 10 10 2 9 3 + 7 n q - 7 n s + 21 n q - 42 n q s + 21 n s + 35 n q 9 2 9 2 9 3 8 4 8 3 - 105 n q s + 105 n q s - 35 n s + 35 n q - 140 n q s 8 2 2 8 3 8 4 7 5 7 4 + 210 n q s - 140 n q s + 35 n s + 21 n q - 105 n q s 7 3 2 7 2 3 7 4 7 5 6 6 + 210 n q s - 210 n q s + 105 n q s - 21 n s + 7 n q 6 5 6 4 2 6 3 3 6 2 4 6 5 - 42 n q s + 105 n q s - 140 n q s + 105 n q s - 42 n q s 6 6 5 7 5 6 5 5 2 5 4 3 5 3 4 + 7 n s + n q - 7 n q s + 21 n q s - 35 n q s + 35 n q s 5 2 5 5 6 5 7 11 10 10 9 2 - 21 n q s + 7 n q s - n s + 3 n + 23 n q - 23 n s + 75 n q 9 9 2 8 3 8 2 8 2 - 150 n q s + 75 n s + 135 n q - 405 n q s + 405 n q s 8 3 7 4 7 3 7 2 2 7 3 - 135 n s + 145 n q - 580 n q s + 870 n q s - 580 n q s 7 4 6 5 6 4 6 3 2 6 2 3 + 145 n s + 93 n q - 465 n q s + 930 n q s - 930 n q s 6 4 6 5 5 6 5 5 5 4 2 + 465 n q s - 93 n s + 33 n q - 198 n q s + 495 n q s 5 3 3 5 2 4 5 5 5 6 4 7 - 660 n q s + 495 n q s - 198 n q s + 33 n s + 5 n q 4 6 4 5 2 4 4 3 4 3 4 4 2 5 - 35 n q s + 105 n q s - 175 n q s + 175 n q s - 105 n q s 4 6 4 7 10 8 2 8 8 2 + 35 n q s - 5 n s - 2 n + 40 n q - 80 n q s + 40 n s 7 3 7 2 7 2 7 3 6 4 + 130 n q - 390 n q s + 390 n q s - 130 n s + 190 n q 6 3 6 2 2 6 3 6 4 5 5 - 760 n q s + 1140 n q s - 760 n q s + 190 n s + 148 n q 5 4 5 3 2 5 2 3 5 4 5 5 - 740 n q s + 1480 n q s - 1480 n q s + 740 n q s - 148 n s 4 6 4 5 4 4 2 4 3 3 4 2 4 + 60 n q - 360 n q s + 900 n q s - 1200 n q s + 900 n q s 4 5 4 6 3 7 3 6 3 5 2 - 360 n q s + 60 n s + 10 n q - 70 n q s + 210 n q s 3 4 3 3 3 4 3 2 5 3 6 3 7 - 350 n q s + 350 n q s - 210 n q s + 70 n q s - 10 n s 9 8 8 7 2 7 7 2 - 16 n - 84 n q + 84 n s - 166 n q + 332 n q s - 166 n s 6 3 6 2 6 2 6 3 5 4 5 3 - 134 n q + 402 n q s - 402 n q s + 134 n s + 4 n q - 16 n q s 5 2 2 5 3 5 4 4 5 4 4 + 24 n q s - 16 n q s + 4 n s + 80 n q - 400 n q s 4 3 2 4 2 3 4 4 4 5 3 6 + 800 n q s - 800 n q s + 400 n q s - 80 n s + 50 n q 3 5 3 4 2 3 3 3 3 2 4 3 5 - 300 n q s + 750 n q s - 1000 n q s + 750 n q s - 300 n q s 3 6 2 7 2 6 2 5 2 2 4 3 + 50 n s + 10 n q - 70 n q s + 210 n q s - 350 n q s 2 3 4 2 2 5 2 6 2 7 8 7 + 350 n q s - 210 n q s + 70 n q s - 10 n s - 14 n - 102 n q 7 6 2 6 6 2 5 3 5 2 + 102 n s - 272 n q + 544 n q s - 272 n s - 344 n q + 1032 n q s 5 2 5 3 4 4 4 3 4 2 2 - 1032 n q s + 344 n s - 205 n q + 820 n q s - 1230 n q s 4 3 4 4 3 5 3 4 3 3 2 + 820 n q s - 205 n s - 35 n q + 175 n q s - 350 n q s 3 2 3 3 4 3 5 2 6 2 5 + 350 n q s - 175 n q s + 35 n s + 15 n q - 90 n q s 2 4 2 2 3 3 2 2 4 2 5 2 6 + 225 n q s - 300 n q s + 225 n q s - 90 n q s + 15 n s 7 6 5 2 4 3 3 4 + 5 n q - 35 n q s + 105 n q s - 175 n q s + 175 n q s 2 5 6 7 7 6 6 5 2 - 105 n q s + 35 n q s - 5 n s + 14 n + 18 n q - 18 n s - 76 n q 5 5 2 4 3 4 2 4 2 + 152 n q s - 76 n s - 200 n q + 600 n q s - 600 n q s 4 3 3 4 3 3 3 2 2 3 3 + 200 n s - 175 n q + 700 n q s - 1050 n q s + 700 n q s 3 4 2 5 2 4 2 3 2 2 2 3 - 175 n s - 59 n q + 295 n q s - 590 n q s + 590 n q s 2 4 2 5 6 5 4 2 3 3 - 295 n q s + 59 n s - 3 n q + 18 n q s - 45 n q s + 60 n q s 2 4 5 6 7 6 5 2 4 3 - 45 n q s + 18 n q s - 3 n s + q - 7 q s + 21 q s - 35 q s 3 4 2 5 6 7 6 5 5 + 35 q s - 21 q s + 7 q s - s + 28 n + 108 n q - 108 n s 4 2 4 4 2 3 3 3 2 3 2 + 130 n q - 260 n q s + 130 n s + 30 n q - 90 n q s + 90 n q s 3 3 2 4 2 3 2 2 2 2 3 - 30 n s - 40 n q + 160 n q s - 240 n q s + 160 n q s 2 4 5 4 3 2 2 3 4 - 40 n s - 22 n q + 110 n q s - 220 n q s + 220 n q s - 110 n q s 5 6 5 4 2 3 3 2 4 5 + 22 n s - 2 q + 12 q s - 30 q s + 40 q s - 30 q s + 12 q s 6 5 4 4 3 2 3 3 2 - 2 s + 8 n + 60 n q - 60 n s + 110 n q - 220 n q s + 110 n s 2 3 2 2 2 2 2 3 4 3 + 70 n q - 210 n q s + 210 n q s - 70 n s + 10 n q - 40 n q s 2 2 3 4 5 4 3 2 2 3 + 60 n q s - 40 n q s + 10 n s - 2 q + 10 q s - 20 q s + 20 q s 4 5 4 3 3 2 2 2 - 10 q s + 2 s - 11 n - 9 n q + 9 n s + 19 n q - 38 n q s 2 2 3 2 2 3 4 3 + 19 n s + 21 n q - 63 n q s + 63 n q s - 21 n s + 4 q - 16 q s 2 2 3 4 3 2 2 2 + 24 q s - 16 q s + 4 s - 9 n - 17 n q + 17 n s - 7 n q + 14 n q s 2 3 2 2 3 2 2 - 7 n s + q - 3 q s + 3 q s - s - 2 n - 4 n q + 4 n s - 2 q + 4 q s 2 8 7 2 7 6 3 - 2 s ) (q + n - s + 1)) - (5 n q + 20 n q - 40 n q s + 30 n q 6 2 6 2 5 4 5 3 5 2 2 - 140 n q s + 140 n q s + 20 n q - 180 n q s + 420 n q s 5 3 4 5 4 4 4 3 2 4 2 3 - 280 n q s + 5 n q - 100 n q s + 450 n q s - 700 n q s 4 4 3 5 3 4 2 3 3 3 3 2 4 + 350 n q s - 20 n q s + 200 n q s - 600 n q s + 700 n q s 3 5 2 5 2 2 4 3 2 3 4 2 2 5 - 280 n q s + 30 n q s - 200 n q s + 450 n q s - 420 n q s 2 6 5 3 4 4 3 5 2 6 + 140 n q s - 20 n q s + 100 n q s - 180 n q s + 140 n q s 7 5 4 4 5 3 6 2 7 8 8 - 40 n q s + 5 q s - 20 q s + 30 q s - 20 q s + 5 q s - 10 n 7 7 6 2 6 6 2 5 3 - 40 n q + 80 n s - 40 n q + 280 n q s - 280 n s + 20 n q 5 2 5 2 5 3 4 4 4 3 + 240 n q s - 840 n q s + 560 n s + 50 n q - 100 n q s 4 2 2 4 3 4 4 3 5 3 4 - 600 n q s + 1400 n q s - 700 n s + 20 n q - 200 n q s 3 3 2 3 2 3 3 4 3 5 2 5 + 200 n q s + 800 n q s - 1400 n q s + 560 n s - 60 n q s 2 4 2 2 3 3 2 2 4 2 5 2 6 + 300 n q s - 200 n q s - 600 n q s + 840 n q s - 280 n s 5 2 4 3 3 4 2 5 6 + 60 n q s - 200 n q s + 100 n q s + 240 n q s - 280 n q s 7 5 3 4 4 3 5 2 6 7 8 + 80 n s - 20 q s + 50 q s - 20 q s - 40 q s + 40 q s - 10 s 7 6 6 5 2 5 5 2 - 10 n - 105 n q + 70 n s - 240 n q + 630 n q s - 210 n s 4 3 4 2 4 2 4 3 3 3 - 175 n q + 1200 n q s - 1575 n q s + 350 n s + 700 n q s 3 2 2 3 3 3 4 2 5 2 3 2 - 2400 n q s + 2100 n q s - 350 n s + 30 n q - 1050 n q s 2 2 3 2 4 2 5 5 3 3 + 2400 n q s - 1575 n q s + 210 n s - 60 n q s + 700 n q s 2 4 5 6 5 2 3 4 2 5 - 1200 n q s + 630 n q s - 70 n s + 30 q s - 175 q s + 240 q s 6 7 6 5 5 4 2 4 - 105 q s + 10 s + 60 n + 90 n q - 360 n s - 150 n q - 450 n q s 4 2 3 3 3 2 3 2 3 3 + 900 n s - 300 n q + 600 n q s + 900 n q s - 1200 n s 2 4 2 3 2 2 2 2 3 2 4 - 100 n q + 900 n q s - 900 n q s - 900 n q s + 900 n s 5 4 3 2 2 3 4 5 + 20 n q + 200 n q s - 900 n q s + 600 n q s + 450 n q s - 360 n s 5 4 2 3 3 2 4 5 6 5 - 20 q s - 100 q s + 300 q s - 150 q s - 90 q s + 60 s + 106 n 4 4 3 2 3 3 2 2 3 + 395 n q - 530 n s + 300 n q - 1580 n q s + 1060 n s - 100 n q 2 2 2 2 2 3 4 3 - 900 n q s + 2370 n q s - 1060 n s - 100 n q + 200 n q s 2 2 3 4 5 4 3 2 + 900 n q s - 1580 n q s + 530 n s + 5 q + 100 q s - 100 q s 2 3 4 5 4 3 3 2 2 - 300 q s + 395 q s - 106 s - 20 n + 260 n q + 80 n s + 420 n q 2 2 2 3 2 2 3 - 780 n q s - 120 n s + 80 n q - 840 n q s + 780 n q s + 80 n s 4 3 2 2 3 4 3 2 - 30 q - 80 q s + 420 q s - 260 q s - 20 s - 150 n - 95 n q 2 2 2 3 2 2 + 450 n s + 160 n q + 190 n q s - 450 n s + 45 q - 160 q s - 95 q s 3 2 2 2 + 150 s - 100 n - 150 n q + 200 n s + 10 q + 150 q s - 100 s - 10 n / 4 \ |d | / - 40 q + 10 s + 6) |--- A[n + 1](r, s)| / ( | 4 | / \ds / 5 4 3 2 5 4 4 3 2 (n + 5 n + 10 n + 10 n + 5 n + 1) (n + 5 n q - 5 n s + 10 n q 3 3 2 2 3 2 2 2 2 2 3 - 20 n q s + 10 n s + 10 n q - 30 n q s + 30 n q s - 10 n s 4 3 2 2 3 4 5 4 + 5 n q - 20 n q s + 30 n q s - 20 n q s + 5 n s + q - 5 q s 3 2 2 3 4 5 4 3 3 2 2 + 10 q s - 10 q s + 5 q s - s - n - 4 n q + 4 n s - 6 n q 2 2 2 3 2 2 3 4 + 12 n q s - 6 n s - 4 n q + 12 n q s - 12 n q s + 4 n s - q 3 2 2 3 4 3 2 2 2 + 4 q s - 6 q s + 4 q s - s - 3 n - 9 n q + 9 n s - 9 n q 2 3 2 2 3 2 + 18 n q s - 9 n s - 3 q + 9 q s - 9 q s + 3 s + n + 2 n q - 2 n s 2 2 5 4 3 2 2 3 + q - 2 q s + s + 2 n + 2 q - 2 s)) - (n - 5 n s + 10 n s - 10 n s 4 5 4 3 2 2 3 4 3 + 5 n s - s + 5 n - 20 n s + 30 n s - 20 n s + 5 s + 10 n 2 2 3 2 2 - 30 n s + 30 n s - 10 s + 10 n - 20 n s + 10 s + 5 n - 5 s + 1) / 5 \ |d | / 6 5 5 5 4 4 4 |--- A[n + 1](r, s)| / (n + n q - n s + 6 n + 5 n q - 5 n s + 15 n | 5 | / \ds / 3 3 3 2 2 2 + 10 n q - 10 n s + 20 n + 10 n q - 10 n s + 15 n + 5 n q - 5 n s + 6 n + q - s + 1) = 0 and in Maple notation -(p^5-4*p^4*r+p^4*s+6*p^3*r^2-4*p^3*r*s-4*p^2*r^3+6*p^2*r^2*s+p*r^4-4*p*r^3*s+r ^4*s-15*p^4+46*p^3*r-14*p^3*s-48*p^2*r^2+42*p^2*r*s+18*p*r^3-42*p*r^2*s-r^4+14* r^3*s+85*p^3-184*p^2*r+71*p^2*s+113*p*r^2-142*p*r*s-14*r^3+71*r^2*s-225*p^2+296 *p*r-154*p*s-71*r^2+154*r*s+274*p-154*r+120*s-120)/(p*r+p*s-r^2-r*s-r-s)/(p-r-1 )^3*A[n](r,s)+(4*p^8-27*p^7*r+5*p^7*s+77*p^6*r^2-35*p^6*r*s-119*p^5*r^3+105*p^5 *r^2*s+105*p^4*r^4-175*p^4*r^3*s-49*p^3*r^5+175*p^3*r^4*s+7*p^2*r^6-105*p^2*r^5 *s+3*p*r^7+35*p*r^6*s-r^8-5*r^7*s-78*p^7+456*p^6*r-90*p^6*s-1098*p^5*r^2+540*p^ 5*r*s+1380*p^4*r^3-1350*p^4*r^2*s-930*p^3*r^4+1800*p^3*r^3*s+288*p^2*r^5-1350*p 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210*p^7*s-2394*p^6*r^2+1470*p^6*r*s+3318*p^5*r^3-4410*p^5*r^2*s-2310*p^4*r^4+ 7350*p^4*r^3*s+378*p^3*r^5-7350*p^3*r^4*s+546*p^2*r^6+4410*p^2*r^5*s-366*p*r^7-\ 1470*p*r^6*s+72*r^8+210*r^7*s+1371*p^7-7722*p^6*r+1875*p^6*s+17541*p^5*r^2-\ 11250*p^5*r*s-19860*p^4*r^3+28125*p^4*r^2*s+10485*p^3*r^4-37500*p^3*r^3*s-666*p ^2*r^5+28125*p^2*r^4*s-1653*p*r^6-11250*p*r^5*s+504*r^7+1875*r^6*s-7725*p^6+ 37035*p^5*r-9315*p^5*s-69300*p^4*r^2+46575*p^4*r*s+61350*p^3*r^3-93150*p^3*r^2* s-22725*p^2*r^4+93150*p^2*r^3*s-225*p*r^5-46575*p*r^4*s+1590*r^6+9315*r^5*s+ 27214*p^5-107846*p^4*r+28224*p^4*s+159244*p^3*r^2-112896*p^3*r*s-102796*p^2*r^3 +169344*p^2*r^2*s+23174*p*r^4-112896*p*r^3*s+1010*r^5+28224*r^4*s-62172*p^4+ 195156*p^3*r-53532*p^3*s-212436*p^2*r^2+160596*p^2*r*s+88092*p*r^3-160596*p*r^2 *s-8640*r^4+53532*r^3*s+92119*p^3-214118*p^2*r+62239*p^2*s+151879*p*r^2-124478* p*r*s-29880*r^3+62239*r^2*s-85365*p^2+130035*p*r-40695*p*s-44670*r^2+40695*r*s+ 44890*p-33390*r+11500*s-10200)/(p^2-2*p*r+r^2-3*p+3*r+2)/(p^3-3*p^2*r+3*p*r^2-r ^3-6*p^2+12*p*r-6*r^2+11*p-11*r-6)/(p^3*r+p^3*s-3*p^2*r^2-3*p^2*r*s+3*p*r^3+3*p *r^2*s-r^4-r^3*s-6*p^2*r-6*p^2*s+12*p*r^2+12*p*r*s-6*r^3-6*r^2*s+11*p*r+11*p*s-\ 11*r^2-11*r*s-6*r-6*s)*diff(diff(A[n](r,s),r),r)+(4*p^8-22*p^7*r+10*p^7*s+42*p^ 6*r^2-70*p^6*r*s-14*p^5*r^3+210*p^5*r^2*s-70*p^4*r^4-350*p^4*r^3*s+126*p^3*r^5+ 350*p^3*r^4*s-98*p^2*r^6-210*p^2*r^5*s+38*p*r^7+70*p*r^6*s-6*r^8-10*r^7*s-90*p^ 7+430*p^6*r-200*p^6*s-690*p^5*r^2+1200*p^5*r*s+150*p^4*r^3-3000*p^4*r^2*s+850*p ^3*r^4+4000*p^3*r^3*s-1110*p^2*r^5-3000*p^2*r^4*s+570*p*r^6+1200*p*r^5*s-110*r^ 7-200*r^6*s+860*p^6-3495*p^5*r+1665*p^5*s+4575*p^4*r^2-8325*p^4*r*s-550*p^3*r^3 +16650*p^3*r^2*s-3750*p^2*r^4-16650*p^2*r^3*s+3165*p*r^5+8325*p*r^4*s-805*r^6-\ 1665*r^5*s-4550*p^5+15275*p^4*r-7475*p^4*s-15600*p^3*r^2+29900*p^3*r*s+650*p^2* r^3-44850*p^2*r^2*s+7150*p*r^4+29900*p*r^3*s-2925*r^5-7475*r^4*s+14546*p^4-\ 38653*p^3*r+19531*p^3*s+28683*p^2*r^2-58593*p^2*r*s+409*p*r^3+58593*p*r^2*s-\ 4985*r^4-19531*r^3*s-28700*p^3+56415*p^2*r-29685*p^2*s-26730*p*r^2+59370*p*r*s-\ 985*r^3-29685*r^2*s+34030*p^2-43750*p*r+24310*p*s+9720*r^2-24310*r*s-22100*p+ 13800*r-8300*s+6000)/(p^4*r+p^4*s-4*p^3*r^2-4*p^3*r*s+6*p^2*r^3+6*p^2*r^2*s-4*p *r^4-4*p*r^3*s+r^5+r^4*s-10*p^3*r-10*p^3*s+30*p^2*r^2+30*p^2*r*s-30*p*r^3-30*p* r^2*s+10*r^4+10*r^3*s+35*p^2*r+35*p^2*s-70*p*r^2-70*p*r*s+35*r^3+35*r^2*s-50*p* r-50*p*s+50*r^2+50*r*s+24*r+24*s)/(p^3-3*p^2*r+3*p*r^2-r^3-6*p^2+12*p*r-6*r^2+ 11*p-11*r-6)*diff(diff(diff(A[n](r,s),r),r),r)-(p^5+5*p^4*s-10*p^3*r^2-20*p^3*r *s+20*p^2*r^3+30*p^2*r^2*s-15*p*r^4-20*p*r^3*s+4*r^5+5*r^4*s-15*p^4-60*p^3*s+90 *p^2*r^2+180*p^2*r*s-120*p*r^3-180*p*r^2*s+45*r^4+60*r^3*s+85*p^3+255*p^2*s-255 *p*r^2-510*p*r*s+170*r^3+255*r^2*s-225*p^2-450*p*s+225*r^2+450*r*s+274*p+274*s-\ 120)/(p^4*r+p^4*s-4*p^3*r^2-4*p^3*r*s+6*p^2*r^3+6*p^2*r^2*s-4*p*r^4-4*p*r^3*s+r 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r+71*n^5*r^2+355*n^4*p^3-710*n^4*p^2*r+355*n^4*p*r^2+710*n^3*p^4-1420*n^3*p^3*r +710*n^3*p^2*r^2+710*n^2*p^5-1420*n^2*p^4*r+710*n^2*p^3*r^2+355*n*p^6-710*n*p^5 *r+355*n*p^4*r^2+71*p^7-142*p^6*r+71*p^5*r^2-154*n^5*p+154*n^5*r-770*n^4*p^2+ 770*n^4*p*r-1540*n^3*p^3+1540*n^3*p^2*r-1540*n^2*p^4+1540*n^2*p^3*r-770*n*p^5+ 770*n*p^4*r-154*p^6+154*p^5*r+120*n^5+600*n^4*p+1200*n^3*p^2+1200*n^2*p^3+600*n *p^4+120*p^5)/(n^5+5*n^4+10*n^3+10*n^2+5*n+1)/(p-r-1)^4/(r+s)*A[n+1](r,s)-(5*n^ 5*p^7-35*n^5*p^6*r+105*n^5*p^5*r^2-175*n^5*p^4*r^3+175*n^5*p^3*r^4-105*n^5*p^2* r^5+35*n^5*p*r^6-5*n^5*r^7+20*n^4*p^8-135*n^4*p^7*r+385*n^4*p^6*r^2-595*n^4*p^5 *r^3+525*n^4*p^4*r^4-245*n^4*p^3*r^5+35*n^4*p^2*r^6+15*n^4*p*r^7-5*n^4*r^8+30*n ^3*p^9-190*n^3*p^8*r+490*n^3*p^7*r^2-630*n^3*p^6*r^3+350*n^3*p^5*r^4+70*n^3*p^4 *r^5-210*n^3*p^3*r^6+110*n^3*p^2*r^7-20*n^3*p*r^8+20*n^2*p^10-110*n^2*p^9*r+210 *n^2*p^8*r^2-70*n^2*p^7*r^3-350*n^2*p^6*r^4+630*n^2*p^5*r^5-490*n^2*p^4*r^6+190 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3+500570*n^3*p^2*r-344370*n^3*p*r^2-18310*n^3*r^3-98720*n^2*p^4-18790*n^2*p^3*r +779040*n^2*p^2*r^2-863730*n^2*p*r^3+202200*n^2*r^4+105515*n*p^5-725015*n*p^4*r +1431240*n*p^3*r^2-911880*n*p^2*r^3+24075*n*p*r^4+76065*n*r^5-12400*p^6+179915* p^5*r-812295*p^4*r^2+1560140*p^3*r^3-1398075*p^2*r^4+564045*p*r^5-81330*r^6-\ 8300*n^5+11050*n^4*p-52550*n^4*r+150750*n^3*p^2-257300*n^3*p*r+23550*n^3*r^2+ 56710*n^2*p^3+282120*n^2*p^2*r-668070*n^2*p*r^2+246240*n^2*r^3-206805*n*p^4+ 940640*n*p^3*r-1128840*n*p^2*r^2+307180*n*p*r^3+46325*n*r^4+41645*p^5-415030*p^ 4*r+1300380*p^3*r^2-1676660*p^2*r^3+915125*p*r^4-173760*r^5-11500*n^4-73140*n^3 *p+27140*n^3*r+25050*n^2*p^2-269520*n^2*p*r+175470*n^2*r^2+246055*n*p^3-688065* n*p^2*r+418545*n*p*r^2-22535*n*r^3-88195*p^4+598835*p^3*r-1242285*p^2*r^2+ 967705*p*r^3-247560*r^4+8200*n^3-42620*n^2*p+67220*n^2*r-166825*n*p^2+248410*n* p*r-56985*n*r^2+116831*p^3-517318*p^2*r+641523*p*r^2-232836*r^3+10600*n^2+56830 *n*p-35630*n*r-92535*p^2+241900*p*r-138765*r^2-7900*n+39570*p-47470*r-7100)/(n^ 3*p^3-3*n^3*p^2*r+3*n^3*p*r^2-n^3*r^3-6*n^3*p^2+12*n^3*p*r-6*n^3*r^2+3*n^2*p^3-\ 9*n^2*p^2*r+9*n^2*p*r^2-3*n^2*r^3+11*n^3*p-11*n^3*r-18*n^2*p^2+36*n^2*p*r-18*n^ 2*r^2+3*n*p^3-9*n*p^2*r+9*n*p*r^2-3*n*r^3-6*n^3+33*n^2*p-33*n^2*r-18*n*p^2+36*n *p*r-18*n*r^2+p^3-3*p^2*r+3*p*r^2-r^3-18*n^2+33*n*p-33*n*r-6*p^2+12*p*r-6*r^2-\ 18*n+11*p-11*r-6)/(n^2+2*n+1)/(r+s)/(p^4-4*p^3*r+6*p^2*r^2-4*p*r^3+r^4-10*p^3+ 30*p^2*r-30*p*r^2+10*r^3+35*p^2-70*p*r+35*r^2-50*p+50*r+24)*diff(diff(diff(A[n+ 1](r,s),r),r),r)+(5*n^5*p^4-20*n^5*p^3*r+30*n^5*p^2*r^2-20*n^5*p*r^3+5*n^5*r^4+ 5*n^4*p^5-50*n^4*p^3*r^2+100*n^4*p^2*r^3-75*n^4*p*r^4+20*n^4*r^5+20*n^3*p^5*r-\ 50*n^3*p^4*r^2+100*n^3*p^2*r^4-100*n^3*p*r^5+30*n^3*r^6+30*n^2*p^5*r^2-100*n^2* p^4*r^3+100*n^2*p^3*r^4-50*n^2*p*r^6+20*n^2*r^7+20*n*p^5*r^3-75*n*p^4*r^4+100*n *p^3*r^5-50*n*p^2*r^6+5*n*r^8+5*p^5*r^4-20*p^4*r^5+30*p^3*r^6-20*p^2*r^7+5*p*r^ 8-60*n^5*p^3+180*n^5*p^2*r-180*n^5*p*r^2+60*n^5*r^3-50*n^4*p^4-100*n^4*p^3*r+ 600*n^4*p^2*r^2-700*n^4*p*r^3+250*n^4*r^4+20*n^3*p^5-300*n^3*p^4*r+400*n^3*p^3* r^2+400*n^3*p^2*r^3-900*n^3*p*r^4+380*n^3*r^5+60*n^2*p^5*r-600*n^2*p^4*r^2+1200 *n^2*p^3*r^3-600*n^2*p^2*r^4-300*n^2*p*r^5+240*n^2*r^6+60*n*p^5*r^2-500*n*p^4*r ^3+1100*n*p^3*r^4-900*n*p^2*r^5+200*n*p*r^6+40*n*r^7+20*p^5*r^3-150*p^4*r^4+340 *p^3*r^5-320*p^2*r^6+120*p*r^7-10*r^8+255*n^5*p^2-510*n^5*p*r+255*n^5*r^2+125*n ^4*p^3+900*n^4*p^2*r-2175*n^4*p*r^2+1150*n^4*r^3-250*n^3*p^4+1500*n^3*p^3*r-450 *n^3*p^2*r^2-2600*n^3*p*r^3+1800*n^3*r^4+30*n^2*p^5-900*n^2*p^4*r+4050*n^2*p^3* r^2-4500*n^2*p^2*r^3+300*n^2*p*r^4+1020*n^2*r^5+60*n*p^5*r-1050*n*p^4*r^2+4100* n*p^3*r^3-5325*n*p^2*r^4+2250*n*p*r^5-35*n*r^6+30*p^5*r^2-400*p^4*r^3+1425*p^3* r^4-1920*p^2*r^5+1015*p*r^6-150*r^7-450*n^5*p+450*n^5*r+150*n^4*p^2-2550*n^4*p* r+2400*n^4*r^2+1100*n^3*p^3-2700*n^3*p^2*r-2400*n^3*p*r^2+4000*n^3*r^3-400*n^2* p^4+4900*n^2*p^3*r-11400*n^2*p^2*r^2+5200*n^2*p*r^3+1700*n^2*r^4+20*n*p^5-900*n *p^4*r+6700*n*p^3*r^2-14300*n*p^2*r^3+9750*n*p*r^4-1270*n*r^5+20*p^5*r-500*p^4* r^2+2900*p^3*r^3-5750*p^2*r^4+4250*p*r^5-920*r^6+274*n^5-880*n^4*p+2250*n^4*r-\ 1950*n^3*p^2+380*n^3*p*r+4310*n^3*r^2+1950*n^2*p^3-11700*n^2*p^2*r+12270*n^2*p* r^2+220*n^2*r^3-275*n*p^4+5000*n*p^3*r-19200*n*p^2*r^2+20980*n*p*r^3-5135*n*r^4 +5*p^5-300*p^4*r+3100*p^3*r^2-9500*p^2*r^3+9995*p*r^4-3026*r^5+770*n^4+980*n^3* p+2100*n^3*r-4200*n^2*p^2+11340*n^2*p*r-2520*n^2*r^2+1400*n*p^3-12600*n*p^2*r+ 23940*n*p*r^2-9660*n*r^3-70*p^4+1680*p^3*r-8820*p^2*r^2+13860*p*r^3-5880*r^4+ 340*n^3+3720*n^2*p-2700*n^2*r-3225*n*p^2+13890*n*p*r-9645*n*r^2+365*p^3-4320*p^ 2*r+11265*p*r^2-6970*r^3-860*n^2+3230*n*p-4950*n*r-870*p^2+4970*p*r-4960*r^2-\ 1030*n+920*p-1950*r-326)/(n^5*p^4-4*n^5*p^3*r+6*n^5*p^2*r^2-4*n^5*p*r^3+n^5*r^4 -10*n^5*p^3+30*n^5*p^2*r-30*n^5*p*r^2+10*n^5*r^3+5*n^4*p^4-20*n^4*p^3*r+30*n^4* p^2*r^2-20*n^4*p*r^3+5*n^4*r^4+35*n^5*p^2-70*n^5*p*r+35*n^5*r^2-50*n^4*p^3+150* n^4*p^2*r-150*n^4*p*r^2+50*n^4*r^3+10*n^3*p^4-40*n^3*p^3*r+60*n^3*p^2*r^2-40*n^ 3*p*r^3+10*n^3*r^4-50*n^5*p+50*n^5*r+175*n^4*p^2-350*n^4*p*r+175*n^4*r^2-100*n^ 3*p^3+300*n^3*p^2*r-300*n^3*p*r^2+100*n^3*r^3+10*n^2*p^4-40*n^2*p^3*r+60*n^2*p^ 2*r^2-40*n^2*p*r^3+10*n^2*r^4+24*n^5-250*n^4*p+250*n^4*r+350*n^3*p^2-700*n^3*p* r+350*n^3*r^2-100*n^2*p^3+300*n^2*p^2*r-300*n^2*p*r^2+100*n^2*r^3+5*n*p^4-20*n* p^3*r+30*n*p^2*r^2-20*n*p*r^3+5*n*r^4+120*n^4-500*n^3*p+500*n^3*r+350*n^2*p^2-\ 700*n^2*p*r+350*n^2*r^2-50*n*p^3+150*n*p^2*r-150*n*p*r^2+50*n*r^3+p^4-4*p^3*r+6 *p^2*r^2-4*p*r^3+r^4+240*n^3-500*n^2*p+500*n^2*r+175*n*p^2-350*n*p*r+175*n*r^2-\ 10*p^3+30*p^2*r-30*p*r^2+10*r^3+240*n^2-250*n*p+250*n*r+35*p^2-70*p*r+35*r^2+ 120*n-50*p+50*r+24)/(r+s)*diff(diff(diff(diff(A[n+1](r,s),r),r),r),r)-(n^5+5*n^ 4*r+10*n^3*r^2+10*n^2*r^3+5*n*r^4+r^5+5*n^4+20*n^3*r+30*n^2*r^2+20*n*r^3+5*r^4+ 10*n^3+30*n^2*r+30*n*r^2+10*r^3+10*n^2+20*n*r+10*r^2+5*n+5*r+1)/(n^5+5*n^4+10*n ^3+10*n^2+5*n+1)/(r+s)*diff(diff(diff(diff(diff(A[n+1](r,s),r),r),r),r),r) = 0 (n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+3*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-6*n^2-12*n *q+12*n*s-6*q^2+12*q*s-6*s^2+11*n+11*q-11*s-6)/(n+q-s)^3*A[n](r,s)-(4*n^5+20*n^ 4*q-20*n^4*s+40*n^3*q^2-80*n^3*q*s+40*n^3*s^2+40*n^2*q^3-120*n^2*q^2*s+120*n^2* q*s^2-40*n^2*s^3+20*n*q^4-80*n*q^3*s+120*n*q^2*s^2-80*n*q*s^3+20*n*s^4+4*q^5-20 *q^4*s+40*q^3*s^2-40*q^2*s^3+20*q*s^4-4*s^5-26*n^4-104*n^3*q+104*n^3*s-156*n^2* q^2+312*n^2*q*s-156*n^2*s^2-104*n*q^3+312*n*q^2*s-312*n*q*s^2+104*n*s^3-26*q^4+ 104*q^3*s-156*q^2*s^2+104*q*s^3-26*s^4+58*n^3+174*n^2*q-174*n^2*s+174*n*q^2-348 *n*q*s+174*n*s^2+58*q^3-174*q^2*s+174*q*s^2-58*s^3-57*n^2-114*n*q+114*n*s-57*q^ 2+114*q*s-57*s^2+29*n+29*q-29*s-6)/(n+q-s)/(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2-n-q+s )^2*diff(A[n](r,s),s)+(6*n^5+30*n^4*q-30*n^4*s+60*n^3*q^2-120*n^3*q*s+60*n^3*s^ 2+60*n^2*q^3-180*n^2*q^2*s+180*n^2*q*s^2-60*n^2*s^3+30*n*q^4-120*n*q^3*s+180*n* q^2*s^2-120*n*q*s^3+30*n*s^4+6*q^5-30*q^4*s+60*q^3*s^2-60*q^2*s^3+30*q*s^4-6*s^ 5-42*n^4-168*n^3*q+168*n^3*s-252*n^2*q^2+504*n^2*q*s-252*n^2*s^2-168*n*q^3+504* n*q^2*s-504*n*q*s^2+168*n*s^3-42*q^4+168*q^3*s-252*q^2*s^2+168*q*s^3-42*s^4+105 *n^3+315*n^2*q-315*n^2*s+315*n*q^2-630*n*q*s+315*n*s^2+105*q^3-315*q^2*s+315*q* s^2-105*s^3-117*n^2-234*n*q+234*n*s-117*q^2+234*q*s-117*s^2+58*n+58*q-58*s-12)/ (n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+3*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-3*n^2-6*n* q+6*n*s-3*q^2+6*q*s-3*s^2+2*n+2*q-2*s)/(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2-n-q+s)* diff(diff(A[n](r,s),s),s)-2*(2*n^3+6*n^2*q-6*n^2*s+6*n*q^2-12*n*q*s+6*n*s^2+2*q ^3-6*q^2*s+6*q*s^2-2*s^3-9*n^2-18*n*q+18*n*s-9*q^2+18*q*s-9*s^2+11*n+11*q-11*s-\ 3)/(n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+3*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-3*n^2-6 *n*q+6*n*s-3*q^2+6*q*s-3*s^2+2*n+2*q-2*s)*diff(diff(diff(A[n](r,s),s),s),s)+ diff(diff(diff(diff(A[n](r,s),s),s),s),s)-(n^4+4*n^3*q-4*n^3*s+6*n^2*q^2-12*n^2 *q*s+6*n^2*s^2+4*n*q^3-12*n*q^2*s+12*n*q*s^2-4*n*s^3+q^4-4*q^3*s+6*q^2*s^2-4*q* s^3+s^4-6*n^3-18*n^2*q+18*n^2*s-18*n*q^2+36*n*q*s-18*n*s^2-6*q^3+18*q^2*s-18*q* s^2+6*s^3+11*n^2+22*n*q-22*n*s+11*q^2-22*q*s+11*s^2-6*n-6*q+6*s)*q^5/(n^2+2*n*q -2*n*s+q^2-2*q*s+s^2+2*n+2*q-2*s+1)^2/(n^5+5*n^4+10*n^3+10*n^2+5*n+1)/(q+n-s+1) *A[n+1](r,s)-(5*n^8*q^4+35*n^7*q^5-40*n^7*q^4*s+105*n^6*q^6-245*n^6*q^5*s+140*n ^6*q^4*s^2+175*n^5*q^7-630*n^5*q^6*s+735*n^5*q^5*s^2-280*n^5*q^4*s^3+175*n^4*q^ 8-875*n^4*q^7*s+1575*n^4*q^6*s^2-1225*n^4*q^5*s^3+350*n^4*q^4*s^4+105*n^3*q^9-\ 700*n^3*q^8*s+1750*n^3*q^7*s^2-2100*n^3*q^6*s^3+1225*n^3*q^5*s^4-280*n^3*q^4*s^ 5+35*n^2*q^10-315*n^2*q^9*s+1050*n^2*q^8*s^2-1750*n^2*q^7*s^3+1575*n^2*q^6*s^4-\ 735*n^2*q^5*s^5+140*n^2*q^4*s^6+5*n*q^11-70*n*q^10*s+315*n*q^9*s^2-700*n*q^8*s^ 3+875*n*q^7*s^4-630*n*q^6*s^5+245*n*q^5*s^6-40*n*q^4*s^7-5*q^11*s+35*q^10*s^2-\ 105*q^9*s^3+175*q^8*s^4-175*q^7*s^5+105*q^6*s^6-35*q^5*s^7+5*q^4*s^8-10*n^8*q^3 -85*n^7*q^4+80*n^7*q^3*s-295*n^6*q^5+595*n^6*q^4*s-280*n^6*q^3*s^2-545*n^5*q^6+ 1770*n^5*q^5*s-1785*n^5*q^4*s^2+560*n^5*q^3*s^3-575*n^4*q^7+2725*n^4*q^6*s-4425 *n^4*q^5*s^2+2975*n^4*q^4*s^3-700*n^4*q^3*s^4-335*n^3*q^8+2300*n^3*q^7*s-5450*n ^3*q^6*s^2+5900*n^3*q^5*s^3-2975*n^3*q^4*s^4+560*n^3*q^3*s^5-85*n^2*q^9+1005*n^ 2*q^8*s-3450*n^2*q^7*s^2+5450*n^2*q^6*s^3-4425*n^2*q^5*s^4+1785*n^2*q^4*s^5-280 *n^2*q^3*s^6+5*n*q^10+170*n*q^9*s-1005*n*q^8*s^2+2300*n*q^7*s^3-2725*n*q^6*s^4+ 1770*n*q^5*s^5-595*n*q^4*s^6+80*n*q^3*s^7+5*q^11-5*q^10*s-85*q^9*s^2+335*q^8*s^ 3-575*q^7*s^4+545*q^6*s^5-295*q^5*s^6+85*q^4*s^7-10*q^3*s^8+10*n^8*q^2+90*n^7*q ^3-80*n^7*q^2*s+305*n^6*q^4-630*n^6*q^3*s+280*n^6*q^2*s^2+495*n^5*q^5-1830*n^5* q^4*s+1890*n^5*q^3*s^2-560*n^5*q^2*s^3+350*n^4*q^6-2475*n^4*q^5*s+4575*n^4*q^4* s^2-3150*n^4*q^3*s^3+700*n^4*q^2*s^4-40*n^3*q^7-1400*n^3*q^6*s+4950*n^3*q^5*s^2 -6100*n^3*q^4*s^3+3150*n^3*q^3*s^4-560*n^3*q^2*s^5-235*n^2*q^8+120*n^2*q^7*s+ 2100*n^2*q^6*s^2-4950*n^2*q^5*s^3+4575*n^2*q^4*s^4-1890*n^2*q^3*s^5+280*n^2*q^2 *s^6-145*n*q^9+470*n*q^8*s-120*n*q^7*s^2-1400*n*q^6*s^3+2475*n*q^5*s^4-1830*n*q ^4*s^5+630*n*q^3*s^6-80*n*q^2*s^7-30*q^10+145*q^9*s-235*q^8*s^2+40*q^7*s^3+350* q^6*s^4-495*q^5*s^5+305*q^4*s^6-90*q^3*s^7+10*q^2*s^8-5*n^8*q-50*n^7*q^2+40*n^7 *q*s-120*n^6*q^3+350*n^6*q^2*s-140*n^6*q*s^2+45*n^5*q^4+720*n^5*q^3*s-1050*n^5* q^2*s^2+280*n^5*q*s^3+600*n^4*q^5-225*n^4*q^4*s-1800*n^4*q^3*s^2+1750*n^4*q^2*s ^3-350*n^4*q*s^4+1020*n^3*q^6-2400*n^3*q^5*s+450*n^3*q^4*s^2+2400*n^3*q^3*s^3-\ 1750*n^3*q^2*s^4+280*n^3*q*s^5+800*n^2*q^7-3060*n^2*q^6*s+3600*n^2*q^5*s^2-450* n^2*q^4*s^3-1800*n^2*q^3*s^4+1050*n^2*q^2*s^5-140*n^2*q*s^6+305*n*q^8-1600*n*q^ 7*s+3060*n*q^6*s^2-2400*n*q^5*s^3+225*n*q^4*s^4+720*n*q^3*s^5-350*n*q^2*s^6+40* n*q*s^7+45*q^9-305*q^8*s+800*q^7*s^2-1020*q^6*s^3+600*q^5*s^4-45*q^4*s^5-120*q^ 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*s^4+18*n*q*s^5-3*n*s^6+q^7-7*q^6*s+21*q^5*s^2-35*q^4*s^3+35*q^3*s^4-21*q^2*s^5 +7*q*s^6-s^7+28*n^6+108*n^5*q-108*n^5*s+130*n^4*q^2-260*n^4*q*s+130*n^4*s^2+30* n^3*q^3-90*n^3*q^2*s+90*n^3*q*s^2-30*n^3*s^3-40*n^2*q^4+160*n^2*q^3*s-240*n^2*q ^2*s^2+160*n^2*q*s^3-40*n^2*s^4-22*n*q^5+110*n*q^4*s-220*n*q^3*s^2+220*n*q^2*s^ 3-110*n*q*s^4+22*n*s^5-2*q^6+12*q^5*s-30*q^4*s^2+40*q^3*s^3-30*q^2*s^4+12*q*s^5 -2*s^6+8*n^5+60*n^4*q-60*n^4*s+110*n^3*q^2-220*n^3*q*s+110*n^3*s^2+70*n^2*q^3-\ 210*n^2*q^2*s+210*n^2*q*s^2-70*n^2*s^3+10*n*q^4-40*n*q^3*s+60*n*q^2*s^2-40*n*q* s^3+10*n*s^4-2*q^5+10*q^4*s-20*q^3*s^2+20*q^2*s^3-10*q*s^4+2*s^5-11*n^4-9*n^3*q +9*n^3*s+19*n^2*q^2-38*n^2*q*s+19*n^2*s^2+21*n*q^3-63*n*q^2*s+63*n*q*s^2-21*n*s ^3+4*q^4-16*q^3*s+24*q^2*s^2-16*q*s^3+4*s^4-9*n^3-17*n^2*q+17*n^2*s-7*n*q^2+14* n*q*s-7*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-2*n^2-4*n*q+4*n*s-2*q^2+4*q*s-2*s^2)/(q+n -s+1)*diff(diff(diff(A[n+1](r,s),s),s),s)-(5*n^8*q+20*n^7*q^2-40*n^7*q*s+30*n^6 *q^3-140*n^6*q^2*s+140*n^6*q*s^2+20*n^5*q^4-180*n^5*q^3*s+420*n^5*q^2*s^2-280*n ^5*q*s^3+5*n^4*q^5-100*n^4*q^4*s+450*n^4*q^3*s^2-700*n^4*q^2*s^3+350*n^4*q*s^4-\ 20*n^3*q^5*s+200*n^3*q^4*s^2-600*n^3*q^3*s^3+700*n^3*q^2*s^4-280*n^3*q*s^5+30*n ^2*q^5*s^2-200*n^2*q^4*s^3+450*n^2*q^3*s^4-420*n^2*q^2*s^5+140*n^2*q*s^6-20*n*q ^5*s^3+100*n*q^4*s^4-180*n*q^3*s^5+140*n*q^2*s^6-40*n*q*s^7+5*q^5*s^4-20*q^4*s^ 5+30*q^3*s^6-20*q^2*s^7+5*q*s^8-10*n^8-40*n^7*q+80*n^7*s-40*n^6*q^2+280*n^6*q*s -280*n^6*s^2+20*n^5*q^3+240*n^5*q^2*s-840*n^5*q*s^2+560*n^5*s^3+50*n^4*q^4-100* n^4*q^3*s-600*n^4*q^2*s^2+1400*n^4*q*s^3-700*n^4*s^4+20*n^3*q^5-200*n^3*q^4*s+ 200*n^3*q^3*s^2+800*n^3*q^2*s^3-1400*n^3*q*s^4+560*n^3*s^5-60*n^2*q^5*s+300*n^2 *q^4*s^2-200*n^2*q^3*s^3-600*n^2*q^2*s^4+840*n^2*q*s^5-280*n^2*s^6+60*n*q^5*s^2 -200*n*q^4*s^3+100*n*q^3*s^4+240*n*q^2*s^5-280*n*q*s^6+80*n*s^7-20*q^5*s^3+50*q ^4*s^4-20*q^3*s^5-40*q^2*s^6+40*q*s^7-10*s^8-10*n^7-105*n^6*q+70*n^6*s-240*n^5* q^2+630*n^5*q*s-210*n^5*s^2-175*n^4*q^3+1200*n^4*q^2*s-1575*n^4*q*s^2+350*n^4*s ^3+700*n^3*q^3*s-2400*n^3*q^2*s^2+2100*n^3*q*s^3-350*n^3*s^4+30*n^2*q^5-1050*n^ 2*q^3*s^2+2400*n^2*q^2*s^3-1575*n^2*q*s^4+210*n^2*s^5-60*n*q^5*s+700*n*q^3*s^3-\ 1200*n*q^2*s^4+630*n*q*s^5-70*n*s^6+30*q^5*s^2-175*q^3*s^4+240*q^2*s^5-105*q*s^ 6+10*s^7+60*n^6+90*n^5*q-360*n^5*s-150*n^4*q^2-450*n^4*q*s+900*n^4*s^2-300*n^3* q^3+600*n^3*q^2*s+900*n^3*q*s^2-1200*n^3*s^3-100*n^2*q^4+900*n^2*q^3*s-900*n^2* q^2*s^2-900*n^2*q*s^3+900*n^2*s^4+20*n*q^5+200*n*q^4*s-900*n*q^3*s^2+600*n*q^2* s^3+450*n*q*s^4-360*n*s^5-20*q^5*s-100*q^4*s^2+300*q^3*s^3-150*q^2*s^4-90*q*s^5 +60*s^6+106*n^5+395*n^4*q-530*n^4*s+300*n^3*q^2-1580*n^3*q*s+1060*n^3*s^2-100*n ^2*q^3-900*n^2*q^2*s+2370*n^2*q*s^2-1060*n^2*s^3-100*n*q^4+200*n*q^3*s+900*n*q^ 2*s^2-1580*n*q*s^3+530*n*s^4+5*q^5+100*q^4*s-100*q^3*s^2-300*q^2*s^3+395*q*s^4-\ 106*s^5-20*n^4+260*n^3*q+80*n^3*s+420*n^2*q^2-780*n^2*q*s-120*n^2*s^2+80*n*q^3-\ 840*n*q^2*s+780*n*q*s^2+80*n*s^3-30*q^4-80*q^3*s+420*q^2*s^2-260*q*s^3-20*s^4-\ 150*n^3-95*n^2*q+450*n^2*s+160*n*q^2+190*n*q*s-450*n*s^2+45*q^3-160*q^2*s-95*q* s^2+150*s^3-100*n^2-150*n*q+200*n*s+10*q^2+150*q*s-100*s^2-10*n-40*q+10*s+6)/(n ^5+5*n^4+10*n^3+10*n^2+5*n+1)/(n^5+5*n^4*q-5*n^4*s+10*n^3*q^2-20*n^3*q*s+10*n^3 *s^2+10*n^2*q^3-30*n^2*q^2*s+30*n^2*q*s^2-10*n^2*s^3+5*n*q^4-20*n*q^3*s+30*n*q^ 2*s^2-20*n*q*s^3+5*n*s^4+q^5-5*q^4*s+10*q^3*s^2-10*q^2*s^3+5*q*s^4-s^5-n^4-4*n^ 3*q+4*n^3*s-6*n^2*q^2+12*n^2*q*s-6*n^2*s^2-4*n*q^3+12*n*q^2*s-12*n*q*s^2+4*n*s^ 3-q^4+4*q^3*s-6*q^2*s^2+4*q*s^3-s^4-3*n^3-9*n^2*q+9*n^2*s-9*n*q^2+18*n*q*s-9*n* s^2-3*q^3+9*q^2*s-9*q*s^2+3*s^3+n^2+2*n*q-2*n*s+q^2-2*q*s+s^2+2*n+2*q-2*s)*diff (diff(diff(diff(A[n+1](r,s),s),s),s),s)-(n^5-5*n^4*s+10*n^3*s^2-10*n^2*s^3+5*n* s^4-s^5+5*n^4-20*n^3*s+30*n^2*s^2-20*n*s^3+5*s^4+10*n^3-30*n^2*s+30*n*s^2-10*s^ 3+10*n^2-20*n*s+10*s^2+5*n-5*s+1)/(n^6+n^5*q-n^5*s+6*n^5+5*n^4*q-5*n^4*s+15*n^4 +10*n^3*q-10*n^3*s+20*n^3+10*n^2*q-10*n^2*s+15*n^2+5*n*q-5*n*s+6*n+q-s+1)*diff( diff(diff(diff(diff(A[n+1](r,s),s),s),s),s),s) = 0 ------------------------------------------------- This took, 3.587, seconds. -------------------------------------------- Theorem: define the Abel-sum type sequence by n ----- \ 6 (k - 1 + p) (n - k + q) k A[n](r, s) = ) binomial(n, k) (r + k) (s - k) x / ----- k = 0 and in Maple notation A[n](r,s) = Sum(binomial(n,k)^6*(r+k)^(k-1+p)*(s-k)^(n-k+q)*x^k,k = 0 .. n) Then we have the following two differential-recurrence equations, relating \ A[n](r,s) and A[n+1](r,s) , the first one with respect to r, the second \ with respect to s 6 5 5 4 2 4 3 3 3 2 2 4 (p - 5 p r + p s + 10 p r - 5 p r s - 10 p r + 10 p r s + 5 p r 2 3 5 4 5 5 4 4 - 10 p r s - p r + 5 p r s - r s - 21 p + 85 p r - 20 p s 3 2 3 2 3 2 2 4 3 - 130 p r + 80 p r s + 90 p r - 120 p r s - 25 p r + 80 p r s 5 4 4 3 3 2 2 2 + r - 20 r s + 175 p - 545 p r + 155 p s + 585 p r - 465 p r s 3 2 4 3 3 2 2 - 235 p r + 465 p r s + 20 r - 155 r s - 735 p + 1625 p r - 580 p s 2 3 2 2 - 1045 p r + 1160 p r s + 155 r - 580 r s + 1624 p - 2204 p r 2 + 1044 p s + 580 r - 1044 r s - 1764 p + 1044 r - 720 s + 720) A[n](r, s) / 2 4 10 9 / ((p r + p s - r - r s - r - s) (p - r - 1) ) - (5 p - 44 p r / 9 8 2 8 7 3 7 2 6 4 + 6 p s + 171 p r - 54 p r s - 384 p r + 216 p r s + 546 p r 6 3 5 5 5 4 4 6 4 5 - 504 p r s - 504 p r + 756 p r s + 294 p r - 756 p r s 3 7 3 6 2 8 2 7 9 8 - 96 p r + 504 p r s + 9 p r - 216 p r s + 4 p r + 54 p r s 10 9 9 8 8 7 2 7 - r - 6 r s - 135 p + 1062 p r - 153 p s - 3636 p r + 1224 p r s 6 3 6 2 5 4 5 3 4 5 + 7056 p r - 4284 p r s - 8442 p r + 8568 p r s + 6300 p r 4 4 3 6 3 5 2 7 2 6 - 10710 p r s - 2772 p r + 8568 p r s + 576 p r - 4284 p r s 8 7 9 8 8 7 + 9 p r + 1224 p r s - 18 r - 153 r s + 1575 p - 10936 p r 7 6 2 6 5 3 5 2 + 1664 p s + 32452 p r - 11648 p r s - 53256 p r + 34944 p r s 4 4 4 3 3 5 3 4 2 6 + 52010 p r - 58240 p r s - 29960 p r + 58240 p r s + 9156 p r 2 5 7 6 8 7 7 - 34944 p r s - 952 p r + 11648 p r s - 89 r - 1664 r s - 10470 p 6 6 5 2 5 4 3 + 63138 p r - 10152 p s - 158958 p r + 60912 p r s + 214170 p r 4 2 3 4 3 3 2 5 - 152280 p r s - 163410 p r + 203040 p r s + 67590 p r 2 4 6 5 7 6 - 152280 p r s - 12378 p r + 60912 p r s + 318 r - 10152 r s 6 5 5 4 2 4 + 44026 p - 225710 p r + 38446 p s + 468160 p r - 192230 p r s 3 3 3 2 2 4 2 3 - 496060 p r + 384460 p r s + 275930 p r - 384460 p r s 5 4 6 5 5 - 71926 p r + 192230 p r s + 5580 r - 38446 r s - 122766 p 4 4 3 2 3 2 3 + 519564 p r - 94266 p s - 850596 p r + 377064 p r s + 662064 p r 2 2 4 3 5 4 - 565596 p r s - 236766 p r + 377064 p r s + 28500 r - 94266 r s 4 3 3 2 2 2 + 230750 p - 772382 p r + 150618 p s + 932646 p r - 451854 p r s 3 2 4 3 3 - 471146 p r + 451854 p r s + 80132 r - 150618 r s - 289665 p 2 2 2 3 + 716886 p r - 152109 p s - 564777 p r + 304218 p r s + 137556 r 2 2 2 - 152109 r s + 233044 p - 377582 p r + 88506 p s + 144538 r - 88506 r s /d \ / - 108684 p + 86004 r - 22680 s + 22320) |-- A[n](r, s)| / ((p - r - 1) ( \dr / / 2 2 2 3 2 2 p r + p s - 2 p r - 2 p r s + r + r s - 3 p r - 3 p s + 3 r + 3 r s 2 2 3 12 11 + 2 r + 2 s) (p - 2 p r + r - 3 p + 3 r + 2) ) + (10 p - 105 p r 11 10 2 10 9 3 9 2 + 15 p s + 495 p r - 165 p r s - 1375 p r + 825 p r s 8 4 8 3 7 5 7 4 6 6 + 2475 p r - 2475 p r s - 2970 p r + 4950 p r s + 2310 p r 6 5 5 7 5 6 4 7 3 9 - 6930 p r s - 990 p r + 6930 p r s - 4950 p r s + 275 p r 3 8 2 10 2 9 11 10 12 + 2475 p r s - 165 p r - 825 p r s + 45 p r + 165 p r s - 5 r 11 11 10 10 9 2 9 - 15 r s - 330 p + 3165 p r - 465 p s - 13500 p r + 4650 p r s 8 3 8 2 7 4 7 3 6 5 + 33525 p r - 20925 p r s - 53100 p r + 55800 p r s + 54810 p r 6 4 5 6 5 5 4 7 - 97650 p r s - 35280 p r + 117180 p r s + 11250 p r 4 6 3 8 3 7 2 9 2 8 - 97650 p r s + 1350 p r + 55800 p r s - 2775 p r - 20925 p r s 10 9 11 10 10 9 + 1020 p r + 4650 p r s - 135 r - 465 r s + 4865 p - 42265 p r 9 8 2 8 7 3 7 2 + 6385 p s + 161460 p r - 57465 p r s - 353940 p r + 229860 p r s 6 4 6 3 5 5 5 4 + 485310 p r - 536340 p r s - 421470 p r + 804510 p r s 4 6 4 5 3 7 3 6 + 217140 p r - 804510 p r s - 47460 p r + 536340 p r s 2 8 2 7 9 8 10 - 10935 p r - 229860 p r s + 8815 p r + 57465 p r s - 1520 r 9 9 8 8 7 2 - 6385 r s - 42405 p + 330300 p r - 51345 p s - 1115820 p r 7 6 3 6 2 5 4 + 410760 p r s + 2124360 p r - 1437660 p r s - 2467710 p r 5 3 4 5 4 4 3 6 + 2875320 p r s + 1748880 p r - 3594150 p r s - 686700 p r 3 5 2 7 2 6 8 + 2875320 p r s + 88920 p r - 1437660 p r s + 29115 p r 7 9 8 8 7 + 410760 p r s - 8940 r - 51345 r s + 243609 p - 1679712 p r 7 6 2 6 5 3 + 269160 p s + 4936932 p r - 1884120 p r s - 7989744 p r 5 2 4 4 4 3 3 5 + 5652360 p r s + 7632030 p r - 9420600 p r s - 4221504 p r 3 4 2 6 2 5 7 + 9420600 p r s + 1168692 p r - 5652360 p r s - 64752 p r 6 8 7 7 6 + 1884120 p r s - 25551 r - 269160 r s - 972585 p + 5840445 p r 6 5 2 5 4 3 - 967650 p s - 14618385 p r + 5805900 p r s + 19525725 p r 4 2 3 4 3 3 2 5 - 14514750 p r s - 14687475 p r + 19353000 p r s + 5909535 p r 2 4 6 5 7 6 - 14514750 p r s - 1002195 p r + 5805900 p r s + 4935 r - 967650 r s 6 5 5 4 2 + 2769331 p - 14176731 p r + 2439255 p s + 29343690 p r 4 3 3 3 2 2 4 - 12196275 p r s - 30994070 p r + 24392550 p r s + 17147415 p r 2 3 5 4 6 - 24392550 p r s - 4419711 p r + 12196275 p r s + 330076 r 5 5 4 4 - 2439255 r s - 5671035 p + 24034710 p r - 4320465 p s 3 2 3 2 3 2 2 - 39428490 p r + 17281860 p r s + 30787560 p r - 25922790 p r s 4 3 5 4 4 - 11073315 p r + 17281860 p r s + 1350570 r - 4320465 r s + 8295441 p 3 3 2 2 2 - 27900693 p r + 5281071 p s + 33929433 p r - 15843213 p r s 3 2 4 3 3 - 17338551 p r + 15843213 p r s + 3014370 r - 5281071 r s - 8459025 p 2 2 2 + 21124560 p r - 4252515 p s - 16872045 p r + 8505030 p r s 3 2 2 + 4206510 r - 4252515 r s + 5711144 p - 9387374 p r + 2034914 p s 2 + 3676230 r - 2034914 r s - 2293020 p + 1853700 r - 439320 s + 414000) / 2 \ |d | / 2 2 3 3 |--- A[n](r, s)| / ((p - 2 p r + r - 3 p + 3 r + 2) (p r + p s | 2 | / \dr / 2 2 2 3 2 4 3 2 2 - 3 p r - 3 p r s + 3 p r + 3 p r s - r - r s - 6 p r - 6 p s 2 3 2 2 + 12 p r + 12 p r s - 6 r - 6 r s + 11 p r + 11 p s - 11 r - 11 r s 2 12 11 11 10 2 - 6 r - 6 s) %2 ) - (10 p - 100 p r + 20 p s + 440 p r 10 9 3 9 2 8 4 8 3 - 220 p r s - 1100 p r + 1100 p r s + 1650 p r - 3300 p r s 7 5 7 4 6 5 5 7 5 6 - 1320 p r + 6600 p r s - 9240 p r s + 1320 p r + 9240 p r s 4 8 4 7 3 9 3 8 2 10 - 1650 p r - 6600 p r s + 1100 p r + 3300 p r s - 440 p r 2 9 11 10 12 11 11 - 1100 p r s + 100 p r + 220 p r s - 10 r - 20 r s - 360 p 10 10 9 2 9 8 3 + 3290 p r - 670 p s - 13100 p r + 6700 p r s + 29250 p r 8 2 7 4 7 3 6 5 - 30150 p r s - 38400 p r + 80400 p r s + 25620 p r 6 4 5 6 5 5 4 7 - 140700 p r s + 2520 p r + 168840 p r s - 21900 p r 4 6 3 8 3 7 2 9 - 140700 p r s + 21000 p r + 80400 p r s - 10350 p r 2 8 10 9 11 10 - 30150 p r s + 2740 p r + 6700 p r s - 310 r - 670 r s 10 9 9 8 2 8 + 5815 p - 48160 p r + 9990 p s + 171765 p r - 89910 p r s 7 3 7 2 6 4 6 3 - 338160 p r + 359640 p r s + 381990 p r - 839160 p r s 5 5 5 4 4 6 4 5 - 206640 p r + 1258740 p r s - 37590 p r - 1258740 p r s 3 7 3 6 2 8 2 7 + 141360 p r + 839160 p r s - 97965 p r - 359640 p r s 9 8 10 9 9 + 31760 p r + 89910 p r s - 4175 r - 9990 r s - 55715 p 8 8 7 2 7 6 3 + 413895 p r - 87540 p s - 1305420 p r + 700320 p r s + 2228940 p r 6 2 5 4 5 3 4 5 - 2451120 p r s - 2117850 p r + 4902240 p r s + 892290 p r 4 4 3 6 3 5 2 7 - 6127800 p r s + 222180 p r + 4902240 p r s - 445380 p r 2 6 8 7 9 8 - 2451120 p r s + 198885 p r + 700320 p r s - 31825 r - 87540 r s 8 7 7 6 2 6 + 352546 p - 2319328 p r + 501040 p s + 6364008 p r - 3507280 p r s 5 3 5 2 4 4 4 3 - 9220736 p r + 10521840 p r s + 7141820 p r - 17536400 p r s 3 5 3 4 2 6 2 5 - 2206176 p r + 17536400 p r s - 650552 p r - 10521840 p r s 7 6 8 7 7 + 686912 p r + 3507280 p r s - 148494 r - 501040 r s - 1551446 p 6 6 5 2 5 + 8892832 p r - 1967290 p s - 20776626 p r + 11803740 p r s 4 3 4 2 3 4 3 3 + 24791260 p r - 29509350 p r s - 14954810 p r + 39345800 p r s 2 5 2 4 6 5 + 3071016 p r - 29509350 p r s + 943618 p r + 11803740 p r s 7 6 6 5 5 - 415844 r - 1967290 r s + 4866475 p - 23789960 p r + 5408890 p s 4 2 4 3 3 3 2 + 45952675 p r - 27044450 p r s - 43240600 p r + 54088900 p r s 2 4 2 3 5 4 + 18908225 p r - 54088900 p r s - 2154400 p r + 27044450 p r s 6 5 5 4 4 - 542415 r - 5408890 r s - 10957055 p + 44367135 p r - 10418140 p s 3 2 3 2 3 2 2 - 67897990 p r + 41672560 p r s + 47061710 p r - 62508840 p r s 4 3 5 4 - 13112715 p r + 41672560 p r s + 538915 r - 10418140 r s 4 3 3 2 2 + 17564794 p - 56472972 p r + 13786204 p s + 64030152 p r 2 3 2 4 - 41358612 p r s - 28900564 p r + 41358612 p r s + 3778590 r 3 3 2 2 - 13786204 r s - 19539504 p + 46669008 p r - 11949504 p s 2 3 2 - 34719504 p r + 23899008 p r s + 7590000 r - 11949504 r s 2 2 + 14309080 p - 22502680 p r + 6115480 p s + 8193600 r - 6115480 r s / 3 \ |d | / - 6189840 p + 4787040 r - 1402800 s + 1195200) |--- A[n](r, s)| / (%2 %1 | 3 | / \dr / 4 4 3 2 3 2 3 2 2 4 3 (p r + p s - 4 p r - 4 p r s + 6 p r + 6 p r s - 4 p r - 4 p r s 5 4 3 3 2 2 2 3 + r + r s - 10 p r - 10 p s + 30 p r + 30 p r s - 30 p r 2 4 3 2 2 2 - 30 p r s + 10 r + 10 r s + 35 p r + 35 p s - 70 p r - 70 p r s 3 2 2 + 35 r + 35 r s - 50 p r - 50 p s + 50 r + 50 r s + 24 r + 24 s)) + ( 10 9 9 8 2 8 7 3 7 2 5 p - 35 p r + 15 p s + 90 p r - 135 p r s - 60 p r + 540 p r s 6 4 6 3 5 5 5 4 4 6 - 210 p r - 1260 p r s + 630 p r + 1890 p r s - 840 p r 4 5 3 7 3 6 2 8 2 7 - 1890 p r s + 660 p r + 1260 p r s - 315 p r - 540 p r s 9 8 10 9 9 8 8 + 85 p r + 135 p r s - 10 r - 15 r s - 165 p + 1035 p r - 450 p s 7 2 7 6 3 6 2 5 4 - 2340 p r + 3600 p r s + 1260 p r - 12600 p r s + 4410 p r 5 3 4 5 4 4 3 6 + 25200 p r s - 10710 p r - 31500 p r s + 11340 p r 3 5 2 7 2 6 8 7 + 25200 p r s - 6660 p r - 12600 p r s + 2115 p r + 3600 p r s 9 8 8 7 7 6 2 - 285 r - 450 r s + 2390 p - 13265 p r + 5855 p s + 25935 p r 6 5 3 5 2 4 4 - 40985 p r s - 10885 p r + 122955 p r s - 37625 p r 4 3 3 5 3 4 2 6 - 204925 p r s + 71085 p r + 204925 p r s - 56035 p r 2 5 7 6 8 7 - 122955 p r s + 21865 p r + 40985 p r s - 3465 r - 5855 r s 7 6 6 5 2 5 - 19980 p + 96540 p r - 43320 p s - 159660 p r + 259920 p r s 4 3 4 2 3 4 3 3 + 49500 p r - 649800 p r s + 167100 p r + 866400 p r s 2 5 2 4 6 5 7 - 230220 p r - 649800 p r s + 120060 p r + 259920 p r s - 23340 r 6 6 5 5 4 2 - 43320 r s + 106569 p - 438789 p r + 200625 p s + 595410 p r 4 3 3 3 2 2 4 - 1003125 p r s - 125130 p r + 2006250 p r s - 407715 p r 2 3 5 4 6 5 - 2006250 p r s + 363711 p r + 1003125 p r s - 94056 r - 200625 r s 5 4 4 3 2 3 - 378189 p + 1288575 p r - 602370 p s - 1372410 p r + 2409480 p r s 2 3 2 2 4 3 + 167670 p r - 3614220 p r s + 518535 p r + 2409480 p r s 5 4 4 3 3 - 224181 r - 602370 r s + 902260 p - 2437975 p r + 1171065 p s 2 2 2 3 2 4 + 1900365 p r - 3513195 p r s - 95845 p r + 3513195 p r s - 268805 r 3 3 2 2 2 - 1171065 r s - 1425210 p + 2855610 p r - 1420020 p s - 1435590 p r 3 2 2 + 2840040 p r s + 5190 r - 1420020 r s + 1422376 p - 1870576 p r 2 + 974176 p s + 448200 r - 974176 r s - 807336 p + 518880 r - 288456 s / 4 \ |d | / 5 5 4 2 4 + 197280) |--- A[n](r, s)| / ((p r + p s - 5 p r - 5 p r s | 4 | / \dr / 3 3 3 2 2 4 2 3 5 4 6 + 10 p r + 10 p r s - 10 p r - 10 p r s + 5 p r + 5 p r s - r 5 4 4 3 2 3 2 3 2 2 - r s - 15 p r - 15 p s + 60 p r + 60 p r s - 90 p r - 90 p r s 4 3 5 4 3 3 2 2 + 60 p r + 60 p r s - 15 r - 15 r s + 85 p r + 85 p s - 255 p r 2 3 2 4 3 2 - 255 p r s + 255 p r + 255 p r s - 85 r - 85 r s - 225 p r 2 2 3 2 - 225 p s + 450 p r + 450 p r s - 225 r - 225 r s + 274 p r + 274 p s 2 6 5 4 2 - 274 r - 274 r s - 120 r - 120 s) %1) - (p + 6 p s - 15 p r 4 3 3 3 2 2 4 2 3 5 - 30 p r s + 40 p r + 60 p r s - 45 p r - 60 p r s + 24 p r 4 6 5 5 4 3 2 3 + 30 p r s - 5 r - 6 r s - 21 p - 105 p s + 210 p r + 420 p r s 2 3 2 2 4 3 5 4 - 420 p r - 630 p r s + 315 p r + 420 p r s - 84 r - 105 r s 4 3 2 2 2 3 2 + 175 p + 700 p s - 1050 p r - 2100 p r s + 1400 p r + 2100 p r s 4 3 3 2 2 - 525 r - 700 r s - 735 p - 2205 p s + 2205 p r + 4410 p r s 3 2 2 2 - 1470 r - 2205 r s + 1624 p + 3248 p s - 1624 r - 3248 r s - 1764 p / 5 \ |d | / 5 5 4 2 4 - 1764 s + 720) |--- A[n](r, s)| / (p r + p s - 5 p r - 5 p r s | 5 | / \dr / 3 3 3 2 2 4 2 3 5 4 6 + 10 p r + 10 p r s - 10 p r - 10 p r s + 5 p r + 5 p r s - r 5 4 4 3 2 3 2 3 2 2 - r s - 15 p r - 15 p s + 60 p r + 60 p r s - 90 p r - 90 p r s 4 3 5 4 3 3 2 2 + 60 p r + 60 p r s - 15 r - 15 r s + 85 p r + 85 p s - 255 p r 2 3 2 4 3 2 - 255 p r s + 255 p r + 255 p r s - 85 r - 85 r s - 225 p r 2 2 3 2 - 225 p s + 450 p r + 450 p r s - 225 r - 225 r s + 274 p r + 274 p s / 6 \ 2 |d | 6 5 - 274 r - 274 r s - 120 r - 120 s) + |--- A[n](r, s)| - (n p | 6 | \dr / 6 4 6 3 2 6 2 3 6 4 6 5 5 6 - 5 n p r + 10 n p r - 10 n p r + 5 n p r - n r + 6 n p 5 5 5 4 2 5 3 3 5 2 4 5 5 - 30 n p r + 60 n p r - 60 n p r + 30 n p r - 6 n p r 4 7 4 6 4 5 2 4 4 3 4 3 4 + 15 n p - 75 n p r + 150 n p r - 150 n p r + 75 n p r 4 2 5 3 8 3 7 3 6 2 3 5 3 - 15 n p r + 20 n p - 100 n p r + 200 n p r - 200 n p r 3 4 4 3 3 5 2 9 2 8 2 7 2 + 100 n p r - 20 n p r + 15 n p - 75 n p r + 150 n p r 2 6 3 2 5 4 2 4 5 10 9 - 150 n p r + 75 n p r - 15 n p r + 6 n p - 30 n p r 8 2 7 3 6 4 5 5 11 10 + 60 n p r - 60 n p r + 30 n p r - 6 n p r + p - 5 p r 9 2 8 3 7 4 6 5 6 4 6 3 + 10 p r - 10 p r + 5 p r - p r - 20 n p + 80 n p r 6 2 2 6 3 6 4 5 5 5 4 - 120 n p r + 80 n p r - 20 n r - 120 n p + 480 n p r 5 3 2 5 2 3 5 4 4 6 4 5 - 720 n p r + 480 n p r - 120 n p r - 300 n p + 1200 n p r 4 4 2 4 3 3 4 2 4 3 7 3 6 - 1800 n p r + 1200 n p r - 300 n p r - 400 n p + 1600 n p r 3 5 2 3 4 3 3 3 4 2 8 2 7 - 2400 n p r + 1600 n p r - 400 n p r - 300 n p + 1200 n p r 2 6 2 2 5 3 2 4 4 9 8 - 1800 n p r + 1200 n p r - 300 n p r - 120 n p + 480 n p r 7 2 6 3 5 4 10 9 8 2 - 720 n p r + 480 n p r - 120 n p r - 20 p + 80 p r - 120 p r 7 3 6 4 6 3 6 2 6 2 6 3 + 80 p r - 20 p r + 155 n p - 465 n p r + 465 n p r - 155 n r 5 4 5 3 5 2 2 5 3 4 5 + 930 n p - 2790 n p r + 2790 n p r - 930 n p r + 2325 n p 4 4 4 3 2 4 2 3 3 6 3 5 - 6975 n p r + 6975 n p r - 2325 n p r + 3100 n p - 9300 n p r 3 4 2 3 3 3 2 7 2 6 + 9300 n p r - 3100 n p r + 2325 n p - 6975 n p r 2 5 2 2 4 3 8 7 6 2 + 6975 n p r - 2325 n p r + 930 n p - 2790 n p r + 2790 n p r 5 3 9 8 7 2 6 3 6 2 - 930 n p r + 155 p - 465 p r + 465 p r - 155 p r - 580 n p 6 6 2 5 3 5 2 5 2 + 1160 n p r - 580 n r - 3480 n p + 6960 n p r - 3480 n p r 4 4 4 3 4 2 2 3 5 3 4 - 8700 n p + 17400 n p r - 8700 n p r - 11600 n p + 23200 n p r 3 3 2 2 6 2 5 2 4 2 7 - 11600 n p r - 8700 n p + 17400 n p r - 8700 n p r - 3480 n p 6 5 2 8 7 6 2 6 + 6960 n p r - 3480 n p r - 580 p + 1160 p r - 580 p r + 1044 n p 6 5 2 5 4 3 4 2 - 1044 n r + 6264 n p - 6264 n p r + 15660 n p - 15660 n p r 3 4 3 3 2 5 2 4 6 + 20880 n p - 20880 n p r + 15660 n p - 15660 n p r + 6264 n p 5 7 6 6 5 4 2 - 6264 n p r + 1044 p - 1044 p r - 720 n - 4320 n p - 10800 n p 3 3 2 4 5 6 / - 14400 n p - 10800 n p - 4320 n p - 720 p ) A[n + 1](r, s) / ( / 6 5 4 3 2 5 (n + 6 n + 15 n + 20 n + 15 n + 6 n + 1) (p - r - 1) (r + s)) + ( 6 9 6 8 6 7 2 6 6 3 6 5 4 6 n p - 54 n p r + 216 n p r - 504 n p r + 756 n p r 6 4 5 6 3 6 6 2 7 6 8 6 9 - 756 n p r + 504 n p r - 216 n p r + 54 n p r - 6 n r 5 10 5 9 5 8 2 5 7 3 5 6 4 + 30 n p - 264 n p r + 1026 n p r - 2304 n p r + 3276 n p r 5 5 5 5 4 6 5 3 7 5 2 8 5 9 - 3024 n p r + 1764 n p r - 576 n p r + 54 n p r + 24 n p r 5 10 4 11 4 10 4 9 2 4 8 3 - 6 n r + 60 n p - 510 n p r + 1890 n p r - 3960 n p r 4 7 4 4 6 5 4 5 6 4 4 7 + 5040 n p r - 3780 n p r + 1260 n p r + 360 n p r 4 3 8 4 2 9 4 10 3 12 3 11 - 540 n p r + 210 n p r - 30 n p r + 60 n p - 480 n p r 3 10 2 3 9 3 3 8 4 3 6 6 + 1620 n p r - 2880 n p r + 2520 n p r - 2520 n p r 3 5 7 3 4 8 3 3 9 3 2 10 2 13 + 2880 n p r - 1620 n p r + 480 n p r - 60 n p r + 30 n p 2 12 2 11 2 2 10 3 2 9 4 - 210 n p r + 540 n p r - 360 n p r - 1260 n p r 2 8 5 2 7 6 2 6 7 2 5 8 + 3780 n p r - 5040 n p r + 3960 n p r - 1890 n p r 2 4 9 2 3 10 14 13 12 2 + 510 n p r - 60 n p r + 6 n p - 24 n p r - 54 n p r 11 3 10 4 9 5 8 6 + 576 n p r - 1764 n p r + 3024 n p r - 3276 n p r 7 7 6 8 5 9 4 10 14 + 2304 n p r - 1026 n p r + 264 n p r - 30 n p r + 6 p r 13 2 12 3 11 4 10 5 9 6 8 7 - 54 p r + 216 p r - 504 p r + 756 p r - 756 p r + 504 p r 7 8 6 9 5 10 6 8 6 7 - 216 p r + 54 p r - 6 p r - 153 n p + 1224 n p r 6 6 2 6 5 3 6 4 4 6 3 5 - 4284 n p r + 8568 n p r - 10710 n p r + 8568 n p r 6 2 6 6 7 6 8 5 9 5 8 - 4284 n p r + 1224 n p r - 153 n r - 774 n p + 6048 n p r 5 7 2 5 6 3 5 5 4 5 4 5 - 20520 n p r + 39312 n p r - 46116 n p r + 33264 n p r 5 3 6 5 2 7 5 8 5 9 4 10 - 13608 n p r + 2160 n p r + 378 n p r - 144 n r - 1560 n p 4 9 4 8 2 4 7 3 4 6 4 + 11730 n p r - 37665 n p r + 66240 n p r - 66780 n p r 4 5 5 4 4 6 4 3 7 4 2 8 + 34020 n p r - 630 n p r - 9360 n p r + 4860 n p r 4 9 4 10 3 11 3 10 3 9 2 - 870 n p r + 15 n r - 1560 n p + 10920 n p r - 31140 n p r 3 8 3 3 7 4 3 6 5 3 5 6 + 43200 n p r - 20160 n p r - 25200 n p r + 47880 n p r 3 4 7 3 3 8 3 2 9 3 10 - 34560 n p r + 12600 n p r - 2040 n p r + 60 n p r 2 12 2 11 2 10 2 2 9 3 - 765 n p + 4500 n p r - 8370 n p r - 3240 n p r 2 8 4 2 7 5 2 6 6 2 5 7 + 39690 n p r - 75600 n p r + 75600 n p r - 44280 n p r 2 4 8 2 3 9 2 2 10 13 12 + 14715 n p r - 2340 n p r + 90 n p r - 138 n p + 264 n p r 11 2 10 3 9 4 8 5 + 2916 n p r - 16272 n p r + 39060 n p r - 54432 n p r 7 6 6 7 5 8 4 9 + 47376 n p r - 25776 n p r + 8262 n p r - 1320 n p r 3 10 14 13 12 2 11 3 + 60 n p r + 6 p - 222 p r + 1575 p r - 5328 p r 10 4 9 5 8 6 7 7 6 8 + 10584 p r - 13356 p r + 10962 p r - 5760 p r + 1818 p r 5 9 4 10 6 7 6 6 6 5 2 - 294 p r + 15 p r + 1664 n p - 11648 n p r + 34944 n p r 6 4 3 6 3 4 6 2 5 6 6 - 58240 n p r + 58240 n p r - 34944 n p r + 11648 n p r 6 7 5 8 5 7 5 6 2 - 1664 n r + 8532 n p - 58272 n p r + 169008 n p r 5 5 3 5 4 4 5 3 5 5 2 6 - 268128 n p r + 247800 n p r - 128352 n p r + 29232 n p r 5 7 5 8 4 9 4 8 + 1632 n p r - 1452 n r + 17340 n p - 113400 n p r 4 7 2 4 6 3 4 5 4 4 4 5 + 307920 n p r - 436800 n p r + 320040 n p r - 72240 n p r 4 3 6 4 2 7 4 8 4 9 - 58800 n p r + 46080 n p r - 10500 n p r + 360 n r 3 10 3 9 3 8 2 3 7 3 + 17300 n p - 103640 n p r + 239580 n p r - 228320 n p r 3 6 4 3 5 5 3 4 6 3 3 7 - 37240 n p r + 300720 n p r - 298760 n p r + 137120 n p r 3 2 8 3 9 3 10 2 11 2 10 - 28380 n p r + 1640 n p r - 20 n r + 8220 n p - 38520 n p r 2 9 2 2 8 3 2 7 4 2 6 5 + 37140 n p r + 128160 n p r - 427560 n p r + 576240 n p r 2 5 6 2 4 7 2 3 8 2 2 9 - 425880 n p r + 176160 n p r - 36660 n p r + 2760 n p r 2 10 12 11 10 2 - 60 n p r + 1224 n p + 1752 n p r - 48156 n p r 9 3 8 4 7 5 6 6 + 185280 n p r - 352800 n p r + 393456 n p r - 266952 n p r 5 7 4 8 3 9 2 10 13 + 107136 n p r - 22920 n p r + 2040 n p r - 60 n p r - 168 p 12 11 2 10 3 9 4 8 5 + 3408 p r - 19572 p r + 55712 p r - 92960 p r + 96768 p r 7 6 6 7 5 8 4 9 3 10 - 63448 p r + 25312 p r - 5592 p r + 560 p r - 20 p r 6 6 6 5 6 4 2 6 3 3 - 10152 n p + 60912 n p r - 152280 n p r + 203040 n p r 6 2 4 6 5 6 6 5 7 - 152280 n p r + 60912 n p r - 10152 n r - 52836 n p 5 6 5 5 2 5 4 3 5 3 4 + 308940 n p r - 744084 n p r + 935580 n p r - 631020 n p r 5 2 5 5 6 5 7 4 8 + 195876 n p r - 4380 n p r - 8076 n r - 108270 n p 4 7 4 6 2 4 5 3 4 4 4 + 601980 n p r - 1334580 n p r + 1429020 n p r - 616800 n p r 4 3 5 4 2 6 4 7 4 8 - 137580 n p r + 232020 n p r - 69420 n p r + 3630 n r 3 9 3 8 3 7 2 3 6 3 - 107280 n p + 532440 n p r - 925800 n p r + 380760 n p r 3 5 4 3 4 5 3 3 6 3 2 7 + 857880 n p r - 1351320 n p r + 809160 n p r - 214200 n p r 3 8 3 9 2 10 2 9 + 18840 n p r - 480 n r - 48285 n p + 161010 n p r 2 8 2 2 7 3 2 6 4 2 5 5 + 74115 n p r - 1123440 n p r + 2251590 n p r - 2187180 n p r 2 4 6 2 3 7 2 2 8 2 9 + 1146990 n p r - 308640 n p r + 35415 n p r - 1590 n p r 2 10 11 10 9 2 + 15 n r - 4542 n p - 46608 n p r + 394050 n p r 8 3 7 4 6 5 5 6 - 1132740 n p r + 1703760 n p r - 1484628 n p r + 755568 n p r 4 7 3 8 2 9 10 12 - 211980 n p r + 28830 n p r - 1740 n p r + 30 n p r + 2049 p 11 10 2 9 3 8 4 7 5 - 29130 p r + 136911 p r - 325020 p r + 448110 p r - 376224 p r 6 6 5 7 4 8 3 9 2 10 + 191490 p r - 56196 p r + 8625 p r - 630 p r + 15 p r 6 5 6 4 6 3 2 6 2 3 + 38446 n p - 192230 n p r + 384460 n p r - 384460 n p r 6 4 6 5 5 6 5 5 + 192230 n p r - 38446 n r + 203244 n p - 988788 n p r 5 4 2 5 3 3 5 2 4 5 5 + 1895280 n p r - 1758120 n p r + 741900 n p r - 66084 n p r 5 6 4 7 4 6 4 5 2 - 27432 n r + 419340 n p - 1919160 n p r + 3285510 n p r 4 4 3 4 3 4 4 2 5 4 6 - 2317050 n p r + 119400 n p r + 670260 n p r - 278490 n p r 4 7 3 8 3 7 3 6 2 + 20190 n r + 409000 n p - 1594640 n p r + 1742920 n p r 3 5 3 3 4 4 3 3 5 3 2 6 + 894840 n p r - 3435600 n p r + 2844000 n p r - 975160 n p r 3 7 3 8 2 9 2 8 + 119480 n p r - 4840 n r + 166350 n p - 270150 n p r 2 7 2 2 6 3 2 5 4 - 1311360 n p r + 4802760 n p r - 6533010 n p r 2 4 5 2 3 6 2 2 7 2 8 + 4471650 n p r - 1559100 n p r + 250260 n p r - 17760 n p r 2 9 10 9 8 2 + 360 n r - 2490 n p + 357600 n p r - 1879350 n p r 7 3 6 4 5 5 4 6 + 4137360 n p r - 4839000 n p r + 3193596 n p r - 1170780 n p r 3 7 2 8 9 10 11 + 223560 n p r - 21270 n p r + 780 n p r - 6 n r - 14382 p 10 9 2 8 3 7 4 + 155712 p r - 599760 p r + 1172830 p r - 1311320 p r 6 5 5 6 4 7 3 8 2 9 + 868048 p r - 335782 p r + 72590 p r - 8350 p r + 420 p r 10 6 4 6 3 6 2 2 - 6 p r - 94266 n p + 377064 n p r - 565596 n p r 6 3 6 4 5 5 5 4 + 377064 n p r - 94266 n r - 505920 n p + 1964004 n p r 5 3 2 5 2 3 5 4 5 5 - 2796816 n p r + 1665624 n p r - 267216 n p r - 59676 n r 4 6 4 5 4 4 2 4 3 3 - 1047030 n p + 3752580 n p r - 4471440 n p r + 1300560 n p r 4 2 4 4 5 4 6 3 7 + 1106610 n p r - 709860 n p r + 68580 n r - 987320 n p 3 6 3 5 2 3 4 3 3 3 4 + 2723120 n p r - 664200 n p r - 4854920 n p r + 6155480 n p r 3 2 5 3 6 3 7 2 8 - 2808000 n p r + 462760 n p r - 26920 n r - 321360 n p 2 7 2 6 2 2 5 3 - 391080 n p r + 5453460 n p r - 11571120 n p r 2 4 4 2 3 5 2 2 6 2 7 + 10822710 n p r - 4964880 n p r + 1078440 n p r - 109800 n p r 2 8 9 8 7 2 + 3630 n r + 95268 n p - 1500132 n p r + 5609448 n p r 6 3 5 4 4 5 3 6 - 9453072 n p r + 8394048 n p r - 4064964 n p r + 1055016 n p r 2 7 8 9 10 9 - 144024 n p r + 8556 n p r - 144 n r + 64685 p - 551582 p r 8 2 7 3 6 4 5 5 + 1732053 p r - 2748992 p r + 2447468 p r - 1258152 p r 4 6 3 7 2 8 9 10 6 3 + 370966 p r - 61264 p r + 4971 p r - 154 p r + r + 150618 n p 6 2 6 2 6 3 5 4 - 451854 n p r + 451854 n p r - 150618 n r + 818904 n p 5 3 5 2 2 5 3 5 4 - 2371908 n p r + 2202300 n p r - 564492 n p r - 84804 n r 4 5 4 4 4 3 2 4 2 3 + 1686060 n p - 4335780 n p r + 2741790 n p r + 928710 n p r 4 4 4 5 3 6 3 5 - 1169970 n p r + 149190 n r + 1476120 n p - 2112480 n p r 3 4 2 3 3 3 3 2 4 3 5 - 3390360 n p r + 8176200 n p r - 5203440 n p r + 1145400 n p r 3 6 2 7 2 6 2 5 2 - 91440 n r + 221580 n p + 2877300 n p r - 11800620 n p r 2 4 3 2 3 4 2 2 5 + 16277340 n p r - 10145190 n p r + 2965050 n p r 2 6 2 7 8 7 - 415650 n p r + 20190 n r - 433224 n p + 3908952 n p r 6 2 5 3 4 4 3 5 - 10804032 n p r + 13740984 n p r - 9037560 n p r + 3171972 n p r 2 6 7 8 9 8 - 597636 n p r + 51996 n p r - 1452 n r - 196482 p + 1335114 p r 7 2 6 3 5 4 4 5 - 3385980 p r + 4299276 p r - 3013668 p r + 1206156 p r 3 6 2 7 8 9 6 2 - 275442 p r + 32670 p r - 1668 p r + 24 r - 152109 n p 6 6 2 5 3 5 2 + 304218 n p r - 152109 n r - 834282 n p + 1590192 n p r 5 2 5 3 4 4 4 3 - 677538 n p r - 78372 n r - 1677765 n p + 2539650 n p r 4 2 2 4 3 4 4 3 5 + 166005 n p r - 1239900 n p r + 212010 n r - 1211500 n p 3 4 3 3 2 3 2 3 3 4 - 653560 n p r + 6386420 n p r - 6165080 n p r + 1842640 n p r 3 5 2 6 2 5 2 4 2 - 198920 n r + 439485 n p - 6271410 n p r + 14698185 n p r 2 3 3 2 2 4 2 5 2 6 - 13211160 n p r + 5284560 n p r - 1008240 n p r + 68580 n r 7 6 5 2 4 3 + 1069242 n p - 6605724 n p r + 13545762 n p r - 12777480 n p r 3 4 2 5 6 7 + 6171900 n p r - 1589316 n p r + 193692 n p r - 8076 n r 8 7 6 2 5 3 4 4 + 414091 p - 2243486 p r + 4549339 p r - 4583424 p r + 2534910 p r 3 5 2 6 7 8 6 - 793548 p r + 131888 p r - 10012 p r + 242 r + 88506 n p 6 5 2 5 5 2 4 3 - 88506 n r + 485610 n p - 440184 n p r - 45426 n r + 904530 n p 4 2 4 2 4 3 3 4 - 285540 n p r - 814920 n p r + 195930 n r + 249460 n p 3 3 3 2 2 3 3 3 4 + 2620280 n p r - 4501500 n p r + 1914440 n p r - 282680 n r 2 5 2 4 2 3 2 2 2 3 - 1299480 n p + 7245780 n p r - 10561140 n p r + 6059640 n p r 2 4 2 5 6 5 - 1593990 n p r + 149190 n r - 1653666 n p + 7323036 n p r 4 2 3 3 2 4 5 - 11061810 n p r + 7708320 n p r - 2751420 n p r + 462972 n p r 6 7 6 5 2 4 3 - 27432 n r - 613498 p + 2640820 p r - 4260942 p r + 3414300 p r 3 4 2 5 6 7 6 - 1487220 p r + 342048 p r - 36854 p r + 1346 r - 22680 n 5 5 4 2 4 4 2 - 121068 n p - 15012 n r - 151575 n p - 302190 n p r + 113565 n r 3 3 3 2 3 2 3 3 + 412020 n p - 1842360 n p r + 1237980 n p r - 261240 n r 2 4 2 3 2 2 2 2 3 + 1487040 n p - 4712100 n p r + 4304610 n p r - 1631760 n p r 2 4 5 4 3 2 + 212010 n r + 1660656 n p - 5329200 n p r + 5946300 n p r 2 3 4 5 6 5 - 3076560 n p r + 722400 n p r - 59676 n r + 643395 p - 2199714 p r 4 2 3 3 2 4 5 6 + 2834685 p r - 1797480 p r + 578970 p r - 87108 p r + 4572 r 5 4 4 3 2 3 - 2160 n - 48330 n p + 37530 n r - 323140 n p + 452960 n p r 3 2 2 3 2 2 2 2 - 151420 n r - 896970 n p + 1721490 n p r - 1042050 n p r 2 3 4 3 2 2 + 195930 n r - 1091844 n p + 2573436 n p r - 2138664 n p r 3 4 5 4 3 2 + 731076 n p r - 84804 n r - 481790 p + 1317106 p r - 1347494 p r 2 3 4 5 4 3 3 + 634606 p r - 134534 p r + 9946 r + 5400 n + 71640 n p - 50040 n r 2 2 2 2 2 3 + 296085 n p - 377250 n p r + 113565 n r + 477222 n p 2 2 3 4 3 - 839496 n p r + 462246 n p r - 78372 n r + 261511 p - 568822 p r 2 2 3 4 3 2 + 433485 p r - 134908 p r + 14134 r - 7200 n - 59130 n p 2 2 2 3 + 37530 n r - 142086 n p + 165912 n p r - 45426 n r - 103218 p 2 2 3 2 + 167568 p r - 84612 p r + 13062 r + 5400 n + 25812 n p - 15012 n r 2 2 + 27983 p - 30154 p r + 7571 r - 2160 n - 4662 p + 2502 r + 360) /d \ / 3 3 |-- A[n + 1](r, s)| / ((r + s) (-r - 2 + p) (p - r - 1) \dr / / 2 2 5 4 3 2 (p - 2 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75050505 r + 927000 n + 1810960 n p + 1897040 n r 2 2 2 2 2 3 - 27922560 n p + 61278000 n p r - 27793440 n r - 44300748 n p 2 2 3 4 + 77057124 n p r - 15779124 n p r - 13269252 n r + 52313882 p 3 2 2 3 4 - 253556276 p r + 418862976 p r - 284501692 p r + 67808110 r 3 2 2 2 + 55200 n + 8536980 n p - 8371380 n r + 15524808 n p - 13975656 n p r 2 3 2 2 - 1383552 n r - 36267310 p + 124326738 p r - 131314566 p r 3 2 2 + 43310338 r - 1103400 n - 3031080 n p + 824280 n r + 16583328 p 2 - 36197736 p r + 18511008 r + 241200 n - 4504420 p + 4745620 r + 551400) / 3 \ |d | / |--- A[n + 1](r, s)| / ((r + s) (-r - 4 + p) (-r - 3 + p) (-r - 2 + p) | 3 | / \dr / 3 2 3 3 3 2 3 2 3 3 (p - r - 1) %1 (n + 3 n + 3 n + 1) (n p - 3 n p r + 3 n p r - n r 3 2 3 3 2 2 3 2 2 2 2 - 6 n p + 12 n p r - 6 n r + 3 n p - 9 n p r + 9 n p r 2 3 3 3 2 2 2 2 2 3 - 3 n r + 11 n p - 11 n r - 18 n p + 36 n p r - 18 n r + 3 n p 2 2 3 3 2 2 2 - 9 n p r + 9 n p r - 3 n r - 6 n + 33 n p - 33 n r - 18 n p 2 3 2 2 3 2 + 36 n p r - 18 n r + p - 3 p r + 3 p r - r - 18 n + 33 n p - 33 n r 2 2 6 9 - 6 p + 12 p r - 6 r - 18 n + 11 p - 11 r - 6)) - (15 n p 6 8 6 7 2 6 6 3 6 5 4 - 135 n p r + 540 n p r - 1260 n p r + 1890 n p r 6 4 5 6 3 6 6 2 7 6 8 6 9 - 1890 n p r + 1260 n p r - 540 n p r + 135 n p r - 15 n r 5 10 5 9 5 8 2 5 7 3 5 6 4 + 30 n p - 210 n p r + 540 n p r - 360 n p r - 1260 n p r 5 5 5 5 4 6 5 3 7 5 2 8 + 3780 n p r - 5040 n p r + 3960 n p r - 1890 n p r 5 9 5 10 4 11 4 10 4 9 2 + 510 n p r - 60 n r + 15 n p - 15 n p r - 450 n p r 4 8 3 4 7 4 4 6 5 4 5 6 + 2250 n p r - 4950 n p r + 5670 n p r - 2520 n p r 4 4 7 4 3 8 4 2 9 4 10 4 11 - 1800 n p r + 3375 n p r - 2175 n p r + 690 n p r - 90 n r 3 11 3 10 2 3 9 3 3 8 4 + 60 n p r - 360 n p r + 600 n p r + 900 n p r 3 7 5 3 6 6 3 5 7 3 4 8 - 5400 n p r + 10080 n p r - 10080 n p r + 5400 n p r 3 3 9 3 2 10 3 11 3 12 2 11 2 - 900 n p r - 600 n p r + 360 n p r - 60 n r + 90 n p r 2 10 3 2 9 4 2 8 5 2 7 6 - 690 n p r + 2175 n p r - 3375 n p r + 1800 n p r 2 6 7 2 5 8 2 4 9 2 3 10 + 2520 n p r - 5670 n p r + 4950 n p r - 2250 n p r 2 2 11 2 12 2 13 11 3 10 4 + 450 n p r + 15 n p r - 15 n r + 60 n p r - 510 n p r 9 5 8 6 7 7 6 8 5 9 + 1890 n p r - 3960 n p r + 5040 n p r - 3780 n p r + 1260 n p r 4 10 3 11 2 12 13 11 4 + 360 n p r - 540 n p r + 210 n p r - 30 n p r + 15 p r 10 5 9 6 8 7 7 8 6 9 - 135 p r + 540 p r - 1260 p r + 1890 p r - 1890 p r 5 10 4 11 3 12 2 13 6 8 + 1260 p r - 540 p r + 135 p r - 15 p r - 450 n p 6 7 6 6 2 6 5 3 6 4 4 + 3600 n p r - 12600 n p r + 25200 n p r - 31500 n p r 6 3 5 6 2 6 6 7 6 8 5 9 + 25200 n p r - 12600 n p r + 3600 n p r - 450 n r - 900 n p 5 8 5 7 2 5 5 4 5 4 5 + 5400 n p r - 10800 n p r + 37800 n p r - 75600 n p r 5 3 6 5 2 7 5 8 5 9 + 75600 n p r - 43200 n p r + 13500 n p r - 1800 n r 4 10 4 9 4 8 2 4 7 3 - 390 n p - 600 n p r + 16200 n p r - 61200 n p r 4 6 4 4 5 5 4 4 6 4 3 7 + 107100 n p r - 90720 n p r + 12600 n p r + 46800 n p r 4 2 8 4 9 4 10 3 11 3 10 - 44550 n p r + 17400 n p r - 2640 n r + 60 n p 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5 6 2 5 5 3 5 4 4 5 3 5 + 80010 n p r + 85890 n p r - 414750 n p r + 577710 n p r 5 2 6 5 7 5 8 4 9 - 411810 n p r + 152790 n p r - 23490 n r + 3900 n p 4 8 4 7 2 4 6 3 4 5 4 + 23100 n p r - 237375 n p r + 687225 n p r - 923475 n p r 4 4 5 4 3 6 4 2 7 4 8 + 508725 n p r + 142275 n p r - 355125 n p r + 184275 n p r 4 9 3 10 3 9 3 8 2 - 33525 n r - 1860 n p + 34200 n p r - 107700 n p r 3 7 3 3 6 4 3 5 5 3 4 6 - 29300 n p r + 738500 n p r - 1624980 n p r + 1693300 n p r 3 3 7 3 2 8 3 9 3 10 - 886300 n p r + 154800 n p r + 47500 n p r - 18160 n r 2 11 2 10 2 9 2 2 8 3 + 90 n p - 6570 n p r + 84150 n p r - 360150 n p r 2 7 4 2 6 5 2 5 6 2 4 7 + 698325 n p r - 534555 n p r - 277935 n p r + 924225 n p r 2 3 8 2 2 9 2 10 2 11 - 794475 n p r + 316425 n p r - 49035 n p r - 495 n r 11 10 2 9 3 8 4 + 180 n p r - 7560 n p r + 81300 n p r - 363000 n p r 7 5 6 6 5 7 4 8 + 860130 n p r - 1181670 n p r + 933450 n p r - 352350 n p r 3 9 2 10 11 12 11 2 - 19950 n p r + 69270 n p r - 21510 n p r + 1710 n r + 90 p r 10 3 9 4 8 5 7 6 6 7 - 2850 p r + 27450 p r - 122010 p r + 306035 p r - 474845 p r 5 8 4 9 3 10 2 11 12 + 472815 p r - 301825 p r + 118735 p r - 26085 p r + 2555 p r 13 6 6 6 5 6 4 2 - 65 r - 43320 n p + 259920 n p r - 649800 n p r 6 3 3 6 2 4 6 5 6 6 + 866400 n p r - 649800 n p r + 259920 n p r - 43320 n r 5 7 5 6 5 5 2 5 4 3 - 84750 n p + 333330 n p r - 220230 n p r - 932550 n p r 5 3 4 5 2 5 5 6 5 7 + 2232150 n p r - 2119050 n p r + 966270 n p r - 175170 n r 4 8 4 7 4 6 2 4 5 3 - 15600 n p - 298950 n p r + 1879650 n p r - 4126350 n p r 4 4 4 4 3 5 4 2 6 4 7 + 3992250 n p r - 961650 n p r - 1285050 n p r + 1057350 n p r 4 8 3 9 3 8 3 7 2 - 241650 n r + 24900 n p - 286500 n p r + 548100 n p r 3 6 3 3 5 4 3 4 5 + 1227300 n p r - 5967300 n p r + 9161100 n p r 3 3 6 3 2 7 3 8 3 9 - 6748500 n p r + 2157900 n p r - 10800 n p r - 106200 n r 2 10 2 9 2 8 2 2 7 3 - 2940 n p + 104100 n p r - 898200 n p r + 2943300 n p r 2 6 4 2 5 5 2 4 6 - 4230300 n p r + 1495980 n p r + 3333900 n p 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4 3 3 5 3 2 6 + 27037800 n p r - 28579200 n p r + 13534020 n p r 3 7 3 8 2 9 2 8 - 1869180 n p r - 310440 n r + 42075 n p - 942075 n p r 2 7 2 2 6 3 2 5 4 + 5879520 n p r - 14517900 n p r + 14101605 n p r 2 4 5 2 3 6 2 2 7 + 2121075 n p r - 15703650 n p r + 12530430 n p r 2 8 2 9 10 9 - 3833550 n p r + 322470 n r - 2010 n p + 104250 n p r 8 2 7 3 6 4 5 5 - 1411200 n p r + 7682880 n p r - 20703990 n p r + 30485430 n p r 4 6 3 7 2 8 9 - 24697500 n p r + 9626100 n p r - 477180 n p r - 745860 n p r 10 11 10 9 2 8 3 + 139080 n r + 15 p - 2175 p r + 63000 p r - 659400 p r 7 4 6 5 5 6 4 7 + 3239520 p r - 8676126 p r + 13757031 p r - 13354665 p r 3 8 2 9 10 11 6 4 + 7880595 p r - 2679885 p r + 461391 p r - 29301 r - 602370 n p 6 3 6 2 2 6 3 6 4 + 2409480 n p r - 3614220 n p r + 2409480 n p r - 602370 n r 5 5 5 4 5 3 2 5 2 3 - 1065384 n p + 1712700 n p r + 3803040 n p r - 11031480 n p r 5 4 5 5 4 6 4 5 + 9129960 n p r - 2548836 n r + 539550 n p - 8564220 n p r 4 4 2 4 3 3 4 2 4 + 25692300 n p r 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3 2 4 2 3 + 22098300 n p r - 44624025 n p r + 27485475 n p r 4 4 4 5 3 6 3 5 + 3609525 n p r - 5948955 n r - 2503140 n p + 4537560 n p r 3 4 2 3 3 3 3 2 4 + 32852700 n p r - 103302300 n p r + 104962200 n p r 3 5 3 6 2 7 2 6 - 39097260 n p r + 2550240 n r + 1816095 n p - 20222085 n p r 2 5 2 2 4 3 2 3 4 + 67472595 n p r - 79601625 n p r + 2124900 n p r 2 2 5 2 6 2 7 8 + 61702380 n p r - 40116090 n p r + 6823830 n r - 253200 n p 7 6 2 5 3 + 5657790 n p r - 40024350 n p r + 125030430 n p r 4 4 3 5 2 6 - 196088850 n p r + 157721040 n p r - 58293060 n p r 7 8 9 8 7 2 + 5193420 n p r + 1056780 n r + 7650 p - 322050 p r + 4117095 p r 6 3 5 4 4 5 3 6 - 22948005 p r + 65679615 p r - 104897385 p r + 96218430 p r 2 7 8 9 6 2 - 49564050 p r + 13040190 p r - 1331490 r - 1420020 n p 6 6 2 5 3 5 2 + 2840040 n p r - 1420020 n r - 1524870 n p - 3945510 n p r 5 2 5 3 4 4 4 3 + 12465630 n p r - 6995250 n r + 6804300 n p - 34841550 n p r 4 2 2 4 3 4 4 3 5 + 42398550 n p r - 7489650 n p r - 6871650 n r + 4185060 n p 3 4 3 3 2 3 2 3 + 6291900 n p r - 82266900 n p r + 138798300 n p r 3 4 3 5 2 6 2 5 - 76888800 n p r + 9880440 n r - 6301980 n p + 50367060 n p r 2 4 2 2 3 3 2 2 4 - 116479800 n p r + 73039500 n p r + 49319100 n p r 2 5 2 6 7 6 - 65860920 n p r + 15917040 n r + 1387110 n p - 22313730 n p r 5 2 4 3 3 4 + 117308250 n p r - 273166950 n p r + 309686700 n p r 2 5 6 7 8 - 166084380 n p r + 33407820 n p r - 224820 n r - 66660 p 7 6 2 5 3 4 4 + 1920390 p r - 17878230 p r + 74859210 p r - 161865750 p r 3 5 2 6 7 8 + 191429940 p r - 123395700 p r + 40028460 p r - 5031660 r 6 6 5 2 5 5 2 + 974176 n p - 974176 n r + 14136 n p + 5816784 n p r - 5830920 n r 4 3 4 2 4 2 4 3 - 10321185 n p + 31034235 n p r - 16492275 n p r - 4220775 n r 3 4 3 3 3 2 2 3 3 - 2823600 n p - 29990340 n p r + 107053980 n p r - 93359020 n p r 3 4 2 5 2 4 2 3 2 + 19118980 n r + 14613885 n p - 81540225 n p r + 118094940 n p r 2 2 3 2 4 2 5 6 - 11040960 n p r - 64498785 n p r + 24371145 n r - 5093730 n p 5 4 2 3 3 + 59790150 n p r - 231015600 n p r + 386750760 n p r 2 4 5 6 7 - 295583550 n p r + 92433906 n p r - 7281936 n r + 373820 p 6 5 2 4 3 3 4 - 7710470 p r + 53026485 p r - 165382675 p r + 262070365 p r 2 5 6 7 6 5 - 216358929 p r + 87525294 p r - 13543890 r - 288456 n + 1001040 n p 5 4 2 4 4 2 - 2731776 n r + 8767740 n p - 12530280 n p r - 564300 n r 3 3 3 2 3 2 3 3 - 2614740 n p + 42915180 n p r - 67975740 n p r + 21906180 n r 2 4 2 3 2 2 2 2 3 - 22267650 n p + 81226380 n p r - 57466800 n p r - 29664540 n p r 2 4 5 4 3 2 + 23845770 n r + 12721980 n p - 108145200 n p r + 297516780 n p r 2 3 4 5 6 - 335827980 n p r + 153081720 n p r - 21078036 n r - 1411626 p 5 4 2 3 3 2 4 + 21191736 p r - 107051940 p r + 241908180 p r - 265388130 p r 5 6 5 4 4 + 136771596 p r - 26308272 r - 547056 n - 3473040 n p + 737760 n r 3 2 3 3 2 2 3 + 6529200 n p - 26950560 n p r + 14950800 n r + 21268215 n p 2 2 2 2 2 3 4 - 44217045 n p r + 3791205 n p r + 13687065 n r - 21458220 n p 3 2 2 3 4 + 128369310 n p r - 236771010 n p r + 160374810 n p r - 33250170 n r 5 4 3 2 2 3 + 3647466 p - 39695550 p r + 143575755 p r - 222499425 p r 4 5 4 3 3 + 151343415 p r - 36918717 r + 295560 n - 4419040 n p + 5601280 n r 2 2 2 2 2 3 - 11577180 n p + 9897240 n p r + 3453300 n r + 23746650 n p 2 2 3 4 - 94394310 n p r + 104291550 n p r - 32461650 n r - 6416760 p 3 2 2 3 4 + 49413690 p r - 121317690 p r + 115642310 p r - 37025990 r 3 2 2 2 + 883680 n + 2978880 n p - 327840 n r - 16261800 n p + 38481360 n p r 2 3 2 2 3 - 19568520 n r + 7488945 p - 38728635 p r + 57969315 p r - 25845945 r 2 2 - 266040 n + 6162576 n p - 6694656 n r - 5489004 p + 17140584 p r 2 - 11917620 r - 996336 n + 2264560 p - 3260896 r - 400776) / 4 \ |d | / 4 4 4 3 4 2 2 4 3 |--- A[n + 1](r, s)| / ((n p - 4 n p r + 6 n p r - 4 n p r | 4 | / \dr / 4 4 4 3 4 2 4 2 4 3 3 4 + n r - 10 n p + 30 n p r - 30 n p r + 10 n r + 4 n p 3 3 3 2 2 3 3 3 4 4 2 4 - 16 n p r + 24 n p r - 16 n p r + 4 n r + 35 n p - 70 n p r 4 2 3 3 3 2 3 2 3 3 2 4 + 35 n r - 40 n p + 120 n p r - 120 n p r + 40 n r + 6 n p 2 3 2 2 2 2 3 2 4 4 4 - 24 n p r + 36 n p r - 24 n p r + 6 n r - 50 n p + 50 n r 3 2 3 3 2 2 3 2 2 + 140 n p - 280 n p r + 140 n r - 60 n p + 180 n p r 2 2 2 3 4 3 2 2 3 - 180 n p r + 60 n r + 4 n p - 16 n p r + 24 n p r - 16 n p r 4 4 3 3 2 2 2 + 4 n r + 24 n - 200 n p + 200 n r + 210 n p - 420 n p r 2 2 3 2 2 3 4 3 + 210 n r - 40 n p + 120 n p r - 120 n p r + 40 n r + p - 4 p r 2 2 3 4 3 2 2 2 + 6 p r - 4 p r + r + 96 n - 300 n p + 300 n r + 140 n p 2 3 2 2 3 2 - 280 n p r + 140 n r - 10 p + 30 p r - 30 p r + 10 r + 144 n 2 2 - 200 n p + 200 n r + 35 p - 70 p r + 35 r + 96 n - 50 p + 50 r + 24) 2 5 4 3 2 2 3 4 5 (n + 2 n + 1) (r + s) (p - 5 p r + 10 p r - 10 p r + 5 p r - r 4 3 2 2 3 4 3 2 - 15 p + 60 p r - 90 p r + 60 p r - 15 r + 85 p - 255 p r 2 3 2 2 + 255 p r - 85 r - 225 p + 450 p r - 225 r + 274 p - 274 r - 120)) + ( 6 5 6 4 6 3 2 6 2 3 6 4 6 5 6 n p - 30 n p r + 60 n p r - 60 n p r + 30 n p r - 6 n r 5 6 5 4 2 5 3 3 5 2 4 5 5 + 6 n p - 90 n p r + 240 n p r - 270 n p r + 144 n p r 5 6 4 6 4 5 2 4 3 4 4 2 5 - 30 n r + 30 n p r - 90 n p r + 300 n p r - 450 n p r 4 6 4 7 3 6 2 3 5 3 3 4 4 + 270 n p r - 60 n r + 60 n p r - 240 n p r + 300 n p r 3 2 6 3 7 3 8 2 6 3 2 5 4 - 300 n p r + 240 n p r - 60 n r + 60 n p r - 270 n p r 2 4 5 2 3 6 2 8 2 9 6 4 + 450 n p r - 300 n p r + 90 n p r - 30 n r + 30 n p r 5 5 4 6 3 7 2 8 10 6 5 - 144 n p r + 270 n p r - 240 n p r + 90 n p r - 6 n r + 6 p r 5 6 4 7 3 8 2 9 10 6 4 - 30 p r + 60 p r - 60 p r + 30 p r - 6 p r - 105 n p 6 3 6 2 2 6 3 6 4 5 5 + 420 n p r - 630 n p r + 420 n p r - 105 n r - 90 n p 5 4 5 3 2 5 2 3 5 4 5 5 - 180 n p r + 1620 n p r - 2880 n p r + 2070 n p r - 540 n r 4 6 4 5 4 4 2 4 3 3 4 2 4 + 30 n p - 630 n p r + 1125 n p r + 1200 n p r - 4500 n p r 4 5 4 6 3 6 3 5 2 3 4 3 + 3870 n p r - 1095 n r + 120 n p r - 1620 n p r + 4200 n p r 3 3 4 3 2 5 3 6 3 7 2 6 2 - 3000 n p r - 1800 n p r + 3180 n p r - 1080 n r + 180 n p r 2 5 3 2 4 4 2 3 5 2 2 6 - 1980 n p r + 5625 n p r - 6300 n p r + 2250 n p r 2 7 2 8 6 3 5 4 4 5 + 720 n p r - 495 n r + 120 n p r - 1170 n p r + 3420 n p r 3 6 2 7 8 9 6 4 - 4380 n p r + 2520 n p r - 450 n p r - 60 n r + 30 p r 5 5 4 6 3 7 2 8 9 10 - 270 p r + 795 p r - 1080 p r + 720 p r - 210 p r + 15 r 6 3 6 2 6 2 6 3 5 4 + 700 n p - 2100 n p r + 2100 n p r - 700 n r + 420 n p 5 3 5 2 2 5 3 5 4 4 5 + 2520 n p r - 10080 n p r + 10920 n p r - 3780 n r - 540 n p 4 4 4 3 2 4 2 3 4 4 + 4800 n p r - 3300 n p r - 13500 n p r + 20400 n p r 4 5 3 6 3 5 3 4 2 3 3 3 - 7860 n r + 60 n p - 2520 n p r + 15900 n p r - 25600 n p r 3 2 4 3 5 3 6 2 6 2 5 2 + 5700 n p r + 14040 n p r - 7580 n r + 180 n p r - 4320 n p r 2 4 3 2 3 4 2 2 5 2 6 + 23100 n p r - 42300 n p r + 28800 n p r - 2580 n p r 2 7 6 2 5 3 4 4 3 5 - 2880 n r + 180 n p r - 3240 n p r + 15600 n p r - 29400 n p r 2 6 7 8 6 3 5 4 + 24300 n p r - 7680 n p r + 240 n r + 60 p r - 900 p r 4 5 3 6 2 7 8 9 6 2 + 4020 p r - 7580 p r + 6720 p r - 2640 p r + 320 r - 2205 n p 6 6 2 5 3 5 2 5 2 + 4410 n p r - 2205 n r - 210 n p - 12600 n p r + 25830 n p r 5 3 4 4 4 3 4 2 2 4 3 - 13020 n r + 3675 n p - 15750 n p r - 7875 n p r + 48300 n p r 4 4 3 5 3 4 3 3 2 - 28350 n r - 1140 n p + 20400 n p r - 72300 n p r 3 2 3 3 4 3 5 2 6 2 5 + 61800 n p r + 17400 n p r - 26160 n r + 60 n p - 3780 n p r 2 4 2 2 3 3 2 2 4 2 5 + 40050 n p r - 125700 n p r + 140625 n p r - 45810 n p r 2 6 6 5 2 4 3 3 4 - 5445 n r + 120 n p r - 4140 n p r + 33600 n p r - 96450 n p r 2 5 6 7 6 2 5 3 + 114120 n p r - 53310 n p r + 6060 n r + 60 p r - 1500 p r 4 4 3 5 2 6 7 8 + 10275 p r - 27510 p r + 32775 p r - 16980 p r + 2880 r 6 6 5 2 5 5 2 + 3248 n p - 3248 n r - 3486 n p + 26460 n p r - 22974 n r 4 3 4 2 4 2 4 3 3 4 - 11550 n p + 17220 n p r + 48930 n p r - 54600 n r + 8400 n p 3 3 3 2 2 3 3 3 4 - 79800 n p r + 154140 n p r - 37520 n p r - 45220 n r 2 5 2 4 2 3 2 2 2 3 - 1170 n p + 31050 n p r - 181800 n p r + 335940 n p r 2 4 2 5 6 5 4 2 - 196110 n p r + 12090 n r + 30 n p - 2520 n p r + 37350 n p r 3 3 2 4 5 6 6 - 171000 n p r + 296220 n p r - 196932 n p r + 36852 n r + 30 p r 5 2 4 3 3 4 2 5 6 - 1350 p r + 14700 p r - 57450 p r + 93714 p r - 64060 p r 7 6 5 5 4 2 4 + 14416 r - 1764 n + 8904 n p - 19488 n r + 15645 n p + 13230 n p r 4 2 3 3 3 2 3 2 - 55335 n r - 30100 n p + 152880 n p r - 126420 n p r 3 3 2 4 2 3 2 2 2 - 31640 n r + 8925 n p - 126000 n p r + 418320 n p r 2 3 2 4 5 4 3 2 - 405300 n p r + 77595 n r - 594 n p + 20820 n p r - 167640 n p r 2 3 4 5 6 5 + 446520 n p r - 425910 n p r + 116220 n r + 6 p - 630 p r 4 2 3 3 2 4 5 6 + 11985 p r - 71860 p r + 165525 p r - 151392 p r + 44602 r 5 4 4 3 2 3 - 6264 n - 4200 n p - 27120 n r + 53340 n p - 123480 n p r 3 2 2 3 2 2 2 2 + 7500 n r - 33600 n p + 260820 n p r - 446040 n p r 2 3 4 3 2 2 3 + 156180 n r + 4620 n p - 85680 n p r + 389340 n p r - 556920 n p r 4 5 4 3 2 2 3 + 217320 n r - 120 p + 5220 p r - 53280 p r + 183060 p r 4 5 4 3 3 2 2 - 230760 p r + 89616 r - 4860 n - 40880 n p + 21440 n r + 64365 n p 2 2 2 3 2 - 251370 n p r + 157845 n r - 17850 n p + 182280 n p r 2 3 4 3 2 2 - 433650 n p r + 249780 n r + 945 p - 21630 p r + 123585 p r 3 4 3 2 2 2 - 226940 p r + 119180 r + 7920 n - 57120 n p + 80880 n r + 35490 n p 2 3 2 2 - 185220 n p r + 173490 n r - 3710 p + 46620 p r - 139230 p r 3 2 2 + 104240 r + 16740 n - 33432 n p + 66912 n r + 7539 p - 48510 p r / 5 \ 2 |d | / + 57711 r + 11016 n - 7336 p + 18352 r + 2556) |--- A[n + 1](r, s)| / ( | 5 | / \dr / 6 5 6 4 6 3 2 6 2 3 6 4 6 5 (n p - 5 n p r + 10 n p r - 10 n p r + 5 n p r - n r 6 4 6 3 6 2 2 6 3 6 4 5 5 - 15 n p + 60 n p r - 90 n p r + 60 n p r - 15 n r + 6 n p 5 4 5 3 2 5 2 3 5 4 5 5 6 3 - 30 n p r + 60 n p r - 60 n p r + 30 n p r - 6 n r + 85 n p 6 2 6 2 6 3 5 4 5 3 - 255 n p r + 255 n p r - 85 n r - 90 n p + 360 n p r 5 2 2 5 3 5 4 4 5 4 4 - 540 n p r + 360 n p r - 90 n r + 15 n p - 75 n p r 4 3 2 4 2 3 4 4 4 5 6 2 + 150 n p r - 150 n p r + 75 n p r - 15 n r - 225 n p 6 6 2 5 3 5 2 5 2 + 450 n p r - 225 n r + 510 n p - 1530 n p r + 1530 n p r 5 3 4 4 4 3 4 2 2 4 3 - 510 n r - 225 n p + 900 n p r - 1350 n p r + 900 n p r 4 4 3 5 3 4 3 3 2 3 2 3 - 225 n r + 20 n p - 100 n p r + 200 n p r - 200 n p r 3 4 3 5 6 6 5 2 5 + 100 n p r - 20 n r + 274 n p - 274 n r - 1350 n p + 2700 n p r 5 2 4 3 4 2 4 2 4 3 - 1350 n r + 1275 n p - 3825 n p r + 3825 n p r - 1275 n r 3 4 3 3 3 2 2 3 3 3 4 - 300 n p + 1200 n p r - 1800 n p r + 1200 n p r - 300 n r 2 5 2 4 2 3 2 2 2 3 2 4 + 15 n p - 75 n p r + 150 n p r - 150 n p r + 75 n p r 2 5 6 5 5 4 2 4 - 15 n r - 120 n + 1644 n p - 1644 n r - 3375 n p + 6750 n p r 4 2 3 3 3 2 3 2 3 3 - 3375 n r + 1700 n p - 5100 n p r + 5100 n p r - 1700 n r 2 4 2 3 2 2 2 2 3 2 4 - 225 n p + 900 n p r - 1350 n p r + 900 n p r - 225 n r 5 4 3 2 2 3 4 5 + 6 n p - 30 n p r + 60 n p r - 60 n p r + 30 n p r - 6 n r 5 4 4 3 2 3 3 2 - 720 n + 4110 n p - 4110 n r - 4500 n p + 9000 n p r - 4500 n r 2 3 2 2 2 2 2 3 4 + 1275 n p - 3825 n p r + 3825 n p r - 1275 n r - 90 n p 3 2 2 3 4 5 4 3 2 + 360 n p r - 540 n p r + 360 n p r - 90 n r + p - 5 p r + 10 p r 2 3 4 5 4 3 3 2 2 - 10 p r + 5 p r - r - 1800 n + 5480 n p - 5480 n r - 3375 n p 2 2 2 3 2 2 + 6750 n p r - 3375 n r + 510 n p - 1530 n p r + 1530 n p r 3 4 3 2 2 3 4 3 - 510 n r - 15 p + 60 p r - 90 p r + 60 p r - 15 r - 2400 n 2 2 2 2 3 + 4110 n p - 4110 n r - 1350 n p + 2700 n p r - 1350 n r + 85 p 2 2 3 2 2 - 255 p r + 255 p r - 85 r - 1800 n + 1644 n p - 1644 n r - 225 p 2 6 5 + 450 p r - 225 r - 720 n + 274 p - 274 r - 120) (r + s)) - (n + 6 n r 4 2 3 3 2 4 5 6 5 4 3 2 + 15 n r + 20 n r + 15 n r + 6 n r + r + 6 n + 30 n r + 60 n r 2 3 4 5 4 3 2 2 3 4 + 60 n r + 30 n r + 6 r + 15 n + 60 n r + 90 n r + 60 n r + 15 r 3 2 2 3 2 2 + 20 n + 60 n r + 60 n r + 20 r + 15 n + 30 n r + 15 r + 6 n + 6 r / 6 \ |d | / + 1) |--- A[n + 1](r, s)| / ( | 6 | / \dr / 6 5 4 3 2 (n + 6 n + 15 n + 20 n + 15 n + 6 n + 1) (r + s)) = 0 4 3 2 2 3 4 3 2 2 3 %1 := p - 4 p r + 6 p r - 4 p r + r - 10 p + 30 p r - 30 p r + 10 r 2 2 + 35 p - 70 p r + 35 r - 50 p + 50 r + 24 3 2 2 3 2 2 %2 := p - 3 p r + 3 p r - r - 6 p + 12 p r - 6 r + 11 p - 11 r - 6 4 3 3 2 2 2 2 2 3 2 - (n + 4 n q - 4 n s + 6 n q - 12 n q s + 6 n s + 4 n q - 12 n q s 2 3 4 3 2 2 3 4 3 + 12 n q s - 4 n s + q - 4 q s + 6 q s - 4 q s + s - 10 n 2 2 2 2 3 2 - 30 n q + 30 n s - 30 n q + 60 n q s - 30 n s - 10 q + 30 q s 2 3 2 2 2 - 30 q s + 10 s + 35 n + 70 n q - 70 n s + 35 q - 70 q s + 35 s / 4 7 6 - 50 n - 50 q + 50 s + 24) A[n](r, s) / (n + q - s) + (5 n + 35 n q / 6 5 2 5 5 2 4 3 4 2 - 35 n s + 105 n q - 210 n q s + 105 n s + 175 n q - 525 n q s 4 2 4 3 3 4 3 3 3 2 2 + 525 n q s - 175 n s + 175 n q - 700 n q s + 1050 n q s 3 3 3 4 2 5 2 4 2 3 2 - 700 n q s + 175 n s + 105 n q - 525 n q s + 1050 n q s 2 2 3 2 4 2 5 6 5 - 1050 n q s + 525 n q s - 105 n s + 35 n q - 210 n q s 4 2 3 3 2 4 5 6 7 + 525 n q s - 700 n q s + 525 n q s - 210 n q s + 35 n s + 5 q 6 5 2 4 3 3 4 2 5 6 7 - 35 q s + 105 q s - 175 q s + 175 q s - 105 q s + 35 q s - 5 s 6 5 5 4 2 4 4 2 - 55 n - 330 n q + 330 n s - 825 n q + 1650 n q s - 825 n s 3 3 3 2 3 2 3 3 2 4 - 1100 n q + 3300 n q s - 3300 n q s + 1100 n s - 825 n q 2 3 2 2 2 2 3 2 4 5 + 3300 n q s - 4950 n q s + 3300 n q s - 825 n s - 330 n q 4 3 2 2 3 4 5 + 1650 n q s - 3300 n q s + 3300 n q s - 1650 n q s + 330 n s 6 5 4 2 3 3 2 4 5 6 - 55 q + 330 q s - 825 q s + 1100 q s - 825 q s + 330 q s - 55 s 5 4 4 3 2 3 3 2 + 230 n + 1150 n q - 1150 n s + 2300 n q - 4600 n q s + 2300 n s 2 3 2 2 2 2 2 3 4 + 2300 n q - 6900 n q s + 6900 n q s - 2300 n s + 1150 n q 3 2 2 3 4 5 - 4600 n q s + 6900 n q s - 4600 n q s + 1150 n s + 230 q 4 3 2 2 3 4 5 4 - 1150 q s + 2300 q s - 2300 q s + 1150 q s - 230 s - 475 n 3 3 2 2 2 2 2 - 1900 n q + 1900 n s - 2850 n q + 5700 n q s - 2850 n s 3 2 2 3 4 3 - 1900 n q + 5700 n q s - 5700 n q s + 1900 n s - 475 q + 1900 q s 2 2 3 4 3 2 2 - 2850 q s + 1900 q s - 475 s + 546 n + 1638 n q - 1638 n s 2 2 3 2 2 + 1638 n q - 3276 n q s + 1638 n s + 546 q - 1638 q s + 1638 q s 3 2 2 2 - 546 s - 379 n - 758 n q + 758 n s - 379 q + 758 q s - 379 s + 146 n /d \ / 3 8 + 146 q - 146 s - 24) |-- A[n](r, s)| / ((n + q - s) %2 ) - (10 n \ds / / 7 7 6 2 6 6 2 5 3 + 80 n q - 80 n s + 280 n q - 560 n q s + 280 n s + 560 n q 5 2 5 2 5 3 4 4 4 3 - 1680 n q s + 1680 n q s - 560 n s + 700 n q - 2800 n q s 4 2 2 4 3 4 4 3 5 3 4 + 4200 n q s - 2800 n q s + 700 n s + 560 n q - 2800 n q s 3 3 2 3 2 3 3 4 3 5 2 6 + 5600 n q s - 5600 n q s + 2800 n q s - 560 n s + 280 n q 2 5 2 4 2 2 3 3 2 2 4 - 1680 n q s + 4200 n q s - 5600 n q s + 4200 n q s 2 5 2 6 7 6 5 2 - 1680 n q s + 280 n s + 80 n q - 560 n q s + 1680 n q s 4 3 3 4 2 5 6 7 - 2800 n q s + 2800 n q s - 1680 n q s + 560 n q s - 80 n s 8 7 6 2 5 3 4 4 3 5 + 10 q - 80 q s + 280 q s - 560 q s + 700 q s - 560 q s 2 6 7 8 7 6 6 5 2 + 280 q s - 80 q s + 10 s - 130 n - 910 n q + 910 n s - 2730 n q 5 5 2 4 3 4 2 4 2 + 5460 n q s - 2730 n s - 4550 n q + 13650 n q s - 13650 n q s 4 3 3 4 3 3 3 2 2 3 3 + 4550 n s - 4550 n q + 18200 n q s - 27300 n q s + 18200 n q s 3 4 2 5 2 4 2 3 2 - 4550 n s - 2730 n q + 13650 n q s - 27300 n q s 2 2 3 2 4 2 5 6 5 + 27300 n q s - 13650 n q s + 2730 n s - 910 n q + 5460 n q s 4 2 3 3 2 4 5 6 - 13650 n q s + 18200 n q s - 13650 n q s + 5460 n q s - 910 n s 7 6 5 2 4 3 3 4 2 5 - 130 q + 910 q s - 2730 q s + 4550 q s - 4550 q s + 2730 q s 6 7 6 5 5 4 2 - 910 q s + 130 s + 685 n + 4110 n q - 4110 n s + 10275 n q 4 4 2 3 3 3 2 3 2 - 20550 n q s + 10275 n s + 13700 n q - 41100 n q s + 41100 n q s 3 3 2 4 2 3 2 2 2 - 13700 n s + 10275 n q - 41100 n q s + 61650 n q s 2 3 2 4 5 4 3 2 - 41100 n q s + 10275 n s + 4110 n q - 20550 n q s + 41100 n q s 2 3 4 5 6 5 - 41100 n q s + 20550 n q s - 4110 n s + 685 q - 4110 q s 4 2 3 3 2 4 5 6 5 + 10275 q s - 13700 q s + 10275 q s - 4110 q s + 685 s - 1915 n 4 4 3 2 3 3 2 - 9575 n q + 9575 n s - 19150 n q + 38300 n q s - 19150 n s 2 3 2 2 2 2 2 3 4 - 19150 n q + 57450 n q s - 57450 n q s + 19150 n s - 9575 n q 3 2 2 3 4 5 + 38300 n q s - 57450 n q s + 38300 n q s - 9575 n s - 1915 q 4 3 2 2 3 4 5 4 + 9575 q s - 19150 q s + 19150 q s - 9575 q s + 1915 s + 3124 n 3 3 2 2 2 2 2 + 12496 n q - 12496 n s + 18744 n q - 37488 n q s + 18744 n s 3 2 2 3 4 + 12496 n q - 37488 n q s + 37488 n q s - 12496 n s + 3124 q 3 2 2 3 4 3 2 - 12496 q s + 18744 q s - 12496 q s + 3124 s - 3076 n - 9228 n q 2 2 2 3 2 + 9228 n s - 9228 n q + 18456 n q s - 9228 n s - 3076 q + 9228 q s 2 3 2 2 - 9228 q s + 3076 s + 1832 n + 3664 n q - 3664 n s + 1832 q - 3664 q s / 2 \ 2 |d | / 3 + 1832 s - 632 n - 632 q + 632 s + 96) |--- A[n](r, s)| / (%2 (n | 2 | / \ds / 2 2 2 2 3 2 2 3 + 3 n q - 3 n s + 3 n q - 6 n q s + 3 n s + q - 3 q s + 3 q s - s 2 2 2 2 7 - 3 n - 6 n q + 6 n s - 3 q + 6 q s - 3 s + 2 n + 2 q - 2 s) ) + (10 n 6 6 5 2 5 5 2 4 3 + 70 n q - 70 n s + 210 n q - 420 n q s + 210 n s + 350 n q 4 2 4 2 4 3 3 4 3 3 - 1050 n q s + 1050 n q s - 350 n s + 350 n q - 1400 n q s 3 2 2 3 3 3 4 2 5 2 4 + 2100 n q s - 1400 n q s + 350 n s + 210 n q - 1050 n q s 2 3 2 2 2 3 2 4 2 5 6 + 2100 n q s - 2100 n q s + 1050 n q s - 210 n s + 70 n q 5 4 2 3 3 2 4 5 - 420 n q s + 1050 n q s - 1400 n q s + 1050 n q s - 420 n q s 6 7 6 5 2 4 3 3 4 + 70 n s + 10 q - 70 q s + 210 q s - 350 q s + 350 q s 2 5 6 7 6 5 5 4 2 - 210 q s + 70 q s - 10 s - 130 n - 780 n q + 780 n s - 1950 n q 4 4 2 3 3 3 2 3 2 + 3900 n q s - 1950 n s - 2600 n q + 7800 n q s - 7800 n q s 3 3 2 4 2 3 2 2 2 2 3 + 2600 n s - 1950 n q + 7800 n q s - 11700 n q s + 7800 n q s 2 4 5 4 3 2 2 3 - 1950 n s - 780 n q + 3900 n q s - 7800 n q s + 7800 n q s 4 5 6 5 4 2 3 3 - 3900 n q s + 780 n s - 130 q + 780 q s - 1950 q s + 2600 q s 2 4 5 6 5 4 4 - 1950 q s + 780 q s - 130 s + 675 n + 3375 n q - 3375 n s 3 2 3 3 2 2 3 2 2 + 6750 n q - 13500 n q s + 6750 n s + 6750 n q - 20250 n q s 2 2 2 3 4 3 2 2 + 20250 n q s - 6750 n s + 3375 n q - 13500 n q s + 20250 n q s 3 4 5 4 3 2 2 3 - 13500 n q s + 3375 n s + 675 q - 3375 q s + 6750 q s - 6750 q s 4 5 4 3 3 2 2 + 3375 q s - 675 s - 1800 n - 7200 n q + 7200 n s - 10800 n q 2 2 2 3 2 2 + 21600 n q s - 10800 n s - 7200 n q + 21600 n q s - 21600 n q s 3 4 3 2 2 3 4 + 7200 n s - 1800 q + 7200 q s - 10800 q s + 7200 q s - 1800 s 3 2 2 2 2 + 2631 n + 7893 n q - 7893 n s + 7893 n q - 15786 n q s + 7893 n s 3 2 2 3 2 + 2631 q - 7893 q s + 7893 q s - 2631 s - 2082 n - 4164 n q 2 2 + 4164 n s - 2082 q + 4164 q s - 2082 s + 828 n + 828 q - 828 s - 144) / 3 \ |d | / 3 2 2 2 2 |--- A[n](r, s)| / (%1 (n + 3 n q - 3 n s + 3 n q - 6 n q s + 3 n s | 3 | / \ds / 3 2 2 3 2 2 2 + q - 3 q s + 3 q s - s - 3 n - 6 n q + 6 n s - 3 q + 6 q s - 3 s 4 3 3 2 2 2 + 2 n + 2 q - 2 s)) - (5 n + 20 n q - 20 n s + 30 n q - 60 n q s 2 2 3 2 2 3 4 3 + 30 n s + 20 n q - 60 n q s + 60 n q s - 20 n s + 5 q - 20 q s 2 2 3 4 3 2 2 2 + 30 q s - 20 q s + 5 s - 40 n - 120 n q + 120 n s - 120 n q 2 3 2 2 3 2 + 240 n q s - 120 n s - 40 q + 120 q s - 120 q s + 40 s + 105 n 2 2 + 210 n q - 210 n s + 105 q - 210 q s + 105 s - 100 n - 100 q + 100 s / 4 \ / 5 \ |d | |d | 5 4 4 + 24) |--- A[n](r, s)|/(%1) + |--- A[n](r, s)| - (n + 5 n q - 5 n s | 4 | | 5 | \ds / \ds / 3 2 3 3 2 2 3 2 2 2 2 + 10 n q - 20 n q s + 10 n s + 10 n q - 30 n q s + 30 n q s 2 3 4 3 2 2 3 4 5 - 10 n s + 5 n q - 20 n q s + 30 n q s - 20 n q s + 5 n s + q 4 3 2 2 3 4 5 4 3 3 - 5 q s + 10 q s - 10 q s + 5 q s - s - 10 n - 40 n q + 40 n s 2 2 2 2 2 3 2 2 - 60 n q + 120 n q s - 60 n s - 40 n q + 120 n q s - 120 n q s 3 4 3 2 2 3 4 3 + 40 n s - 10 q + 40 q s - 60 q s + 40 q s - 10 s + 35 n 2 2 2 2 3 2 + 105 n q - 105 n s + 105 n q - 210 n q s + 105 n s + 35 q - 105 q s 2 3 2 2 2 + 105 q s - 35 s - 50 n - 100 n q + 100 n s - 50 q + 100 q s - 50 s 6 / + 24 n + 24 q - 24 s) q A[n + 1](r, s) / ( / 6 5 4 3 2 6 10 5 (n + 6 n + 15 n + 20 n + 15 n + 6 n + 1) (q + n - s + 1) ) - (6 n q 9 6 9 5 8 7 8 6 8 5 2 + 54 n q - 60 n q s + 216 n q - 486 n q s + 270 n q s 7 8 7 7 7 6 2 7 5 3 6 9 + 504 n q - 1728 n q s + 1944 n q s - 720 n q s + 756 n q 6 8 6 7 2 6 6 3 6 5 4 - 3528 n q s + 6048 n q s - 4536 n q s + 1260 n q s 5 10 5 9 5 8 2 5 7 3 + 756 n q - 4536 n q s + 10584 n q s - 12096 n q s 5 6 4 5 5 5 4 11 4 10 + 6804 n q s - 1512 n q s + 504 n q - 3780 n q s 4 9 2 4 8 3 4 7 4 4 6 5 + 11340 n q s - 17640 n q s + 15120 n q s - 6804 n q s 4 5 6 3 12 3 11 3 10 2 + 1260 n q s + 216 n q - 2016 n q s + 7560 n q s 3 9 3 3 8 4 3 7 5 3 6 6 - 15120 n q s + 17640 n q s - 12096 n q s + 4536 n q s 3 5 7 2 13 2 12 2 11 2 - 720 n q s + 54 n q - 648 n q s + 3024 n q s 2 10 3 2 9 4 2 8 5 2 7 6 - 7560 n q s + 11340 n q s - 10584 n q s + 6048 n q s 2 6 7 2 5 8 14 13 12 2 - 1944 n q s + 270 n q s + 6 n q - 108 n q s + 648 n q s 11 3 10 4 9 5 8 6 - 2016 n q s + 3780 n q s - 4536 n q s + 3528 n q s 7 7 6 8 5 9 14 13 2 - 1728 n q s + 486 n q s - 60 n q s - 6 q s + 54 q s 12 3 11 4 10 5 9 6 8 7 7 8 - 216 q s + 504 q s - 756 q s + 756 q s - 504 q s + 216 q s 6 9 5 10 10 4 9 5 9 4 8 6 - 54 q s + 6 q s - 15 n q - 174 n q + 150 n q s - 846 n q 8 5 8 4 2 7 7 7 6 7 5 2 + 1566 n q s - 675 n q s - 2304 n q + 6768 n q s - 6264 n q s 7 4 3 6 8 6 7 6 6 2 + 1800 n q s - 3906 n q + 16128 n q s - 23688 n q s 6 5 3 6 4 4 5 9 5 8 + 14616 n q s - 3150 n q s - 4284 n q + 23436 n q s 5 7 2 5 6 3 5 5 4 5 4 5 - 48384 n q s + 47376 n q s - 21924 n q s + 3780 n q s 4 10 4 9 4 8 2 4 7 3 - 3024 n q + 21420 n q s - 58590 n q s + 80640 n q s 4 6 4 4 5 5 4 4 6 3 11 - 59220 n q s + 21924 n q s - 3150 n q s - 1296 n q 3 10 3 9 2 3 8 3 3 7 4 + 12096 n q s - 42840 n q s + 78120 n q s - 80640 n q s 3 6 5 3 5 6 3 4 7 2 12 + 47376 n q s - 14616 n q s + 1800 n q s - 279 n q 2 11 2 10 2 2 9 3 2 8 4 + 3888 n q s - 18144 n q s + 42840 n q s - 58590 n q s 2 7 5 2 6 6 2 5 7 2 4 8 13 + 48384 n q s - 23688 n q s + 6264 n q s - 675 n q s - 6 n q 12 11 2 10 3 9 4 + 558 n q s - 3888 n q s + 12096 n q s - 21420 n q s 8 5 7 6 6 7 5 8 + 23436 n q s - 16128 n q s + 6768 n q s - 1566 n q s 4 9 14 13 12 2 11 3 10 4 + 150 n q s + 6 q + 6 q s - 279 q s + 1296 q s - 3024 q s 9 5 8 6 7 7 6 8 5 9 4 10 + 4284 q s - 3906 q s + 2304 q s - 846 q s + 174 q s - 15 q s 10 3 9 4 9 3 8 5 8 4 + 20 n q + 260 n q - 200 n q s + 1380 n q - 2340 n q s 8 3 2 7 6 7 5 7 4 2 + 900 n q s + 4000 n q - 11040 n q s + 9360 n q s 7 3 3 6 7 6 6 6 5 2 - 2400 n q s + 7000 n q - 28000 n q s + 38640 n q s 6 4 3 6 3 4 5 8 5 7 - 21840 n q s + 4200 n q s + 7560 n q - 42000 n q s 5 6 2 5 5 3 5 4 4 5 3 5 + 84000 n q s - 77280 n q s + 32760 n q s - 5040 n q s 4 9 4 8 4 7 2 4 6 3 + 4760 n q - 37800 n q s + 105000 n q s - 140000 n q s 4 5 4 4 4 5 4 3 6 3 10 + 96600 n q s - 32760 n q s + 4200 n q s + 1280 n q 3 9 3 8 2 3 7 3 3 6 4 - 19040 n q s + 75600 n q s - 140000 n q s + 140000 n q s 3 5 5 3 4 6 3 3 7 2 11 - 77280 n q s + 21840 n q s - 2400 n q s - 300 n q 2 10 2 9 2 2 8 3 2 7 4 - 3840 n q s + 28560 n q s - 75600 n q s + 105000 n q s 2 6 5 2 5 6 2 4 7 2 3 8 - 84000 n q s + 38640 n q s - 9360 n q s + 900 n q s 12 11 10 2 9 3 8 4 - 300 n q + 600 n q s + 3840 n q s - 19040 n q s + 37800 n q s 7 5 6 6 5 7 4 8 - 42000 n q s + 28000 n q s - 11040 n q s + 2340 n q s 3 9 13 12 11 2 10 3 9 4 - 200 n q s - 60 q + 300 q s - 300 q s - 1280 q s + 4760 q s 8 5 7 6 6 7 5 8 4 9 - 7560 q s + 7000 q s - 4000 q s + 1380 q s - 260 q s 3 10 10 2 9 3 9 2 8 4 + 20 q s - 15 n q - 230 n q + 150 n q s - 1245 n q 8 3 8 2 2 7 5 7 4 7 3 2 + 2070 n q s - 675 n q s - 3300 n q + 9960 n q s - 8280 n q s 7 2 3 6 6 6 5 6 4 2 + 1800 n q s - 4450 n q + 23100 n q s - 34860 n q s 6 3 3 6 2 4 5 7 5 6 + 19320 n q s - 3150 n q s - 1920 n q + 26700 n q s 5 5 2 5 4 3 5 3 4 5 2 5 - 69300 n q s + 69720 n q s - 28980 n q s + 3780 n q s 4 8 4 7 4 6 2 4 5 3 + 2970 n q + 9600 n q s - 66750 n q s + 115500 n q s 4 4 4 4 3 5 4 2 6 3 9 - 87150 n q s + 28980 n q s - 3150 n q s + 5380 n q 3 8 3 7 2 3 6 3 3 5 4 - 11880 n q s - 19200 n q s + 89000 n q s - 115500 n q s 3 4 5 3 3 6 3 2 7 2 10 + 69720 n q s - 19320 n q s + 1800 n q s + 3825 n q 2 9 2 8 2 2 7 3 2 6 4 - 16140 n q s + 17820 n q s + 19200 n q s - 66750 n q s 2 5 5 2 4 6 2 3 7 2 2 8 + 69300 n q s - 34860 n q s + 8280 n q s - 675 n q s 11 10 9 2 8 3 7 4 + 1350 n q - 7650 n q s + 16140 n q s - 11880 n q s - 9600 n q s 6 5 5 6 4 7 3 8 + 26700 n q s - 23100 n q s + 9960 n q s - 2070 n q s 2 9 12 11 10 2 9 3 + 150 n q s + 195 q - 1350 q s + 3825 q s - 5380 q s 8 4 7 5 6 6 5 7 4 8 + 2970 q s + 1920 q s - 4450 q s + 3300 q s - 1245 q s 3 9 2 10 10 9 2 9 8 3 + 230 q s - 15 q s + 6 n q + 120 n q - 60 n q s + 610 n q 8 2 8 2 7 4 7 3 7 2 2 - 1080 n q s + 270 n q s + 830 n q - 4880 n q s + 4320 n q s 7 3 6 5 6 4 6 3 2 - 720 n q s - 2066 n q - 5810 n q s + 17080 n q s 6 2 3 6 4 5 6 5 5 - 10080 n q s + 1260 n q s - 9224 n q + 12396 n q s 5 4 2 5 3 3 5 2 4 5 5 + 17430 n q s - 34160 n q s + 15120 n q s - 1512 n q s 4 7 4 6 4 5 2 4 4 3 - 14920 n q + 46120 n q s - 30990 n q s - 29050 n q s 4 3 4 4 2 5 4 6 3 8 + 42700 n q s - 15120 n q s + 1260 n q s - 13010 n q 3 7 3 6 2 3 5 3 3 4 4 + 59680 n q s - 92240 n q s + 41320 n q s + 29050 n q s 3 3 5 3 2 6 3 7 2 9 - 34160 n q s + 10080 n q s - 720 n q s - 6360 n q 2 8 2 7 2 2 6 3 2 5 4 + 39030 n q s - 89520 n q s + 92240 n q s - 30990 n q s 2 4 5 2 3 6 2 2 7 2 8 - 17430 n q s + 17080 n q s - 4320 n q s + 270 n q s 10 9 8 2 7 3 - 1596 n q + 12720 n q s - 39030 n q s + 59680 n q s 6 4 5 5 4 6 3 7 - 46120 n q s + 12396 n q s + 5810 n q s - 4880 n q s 2 8 9 11 10 9 2 + 1080 n q s - 60 n q s - 150 q + 1596 q s - 6360 q s 8 3 7 4 6 5 5 6 4 7 + 13010 q s - 14920 q s + 9224 q s - 2066 q s - 830 q s 3 8 2 9 10 10 9 9 8 2 + 610 q s - 120 q s + 6 q s - n - 34 n q + 10 n s - 111 n q 8 8 2 7 3 7 2 7 2 + 306 n q s - 45 n s + 816 n q + 888 n q s - 1224 n q s 7 3 6 4 6 3 6 2 2 6 3 + 120 n s + 5214 n q - 5712 n q s - 3108 n q s + 2856 n q s 6 4 5 5 5 4 5 3 2 5 2 3 - 210 n s + 11664 n q - 31284 n q s + 17136 n q s + 6216 n q s 5 4 5 5 4 6 4 5 4 4 2 - 4284 n q s + 252 n s + 12540 n q - 58320 n q s + 78210 n q s 4 3 3 4 2 4 4 5 4 6 3 7 - 28560 n q s - 7770 n q s + 4284 n q s - 210 n s + 5760 n q 3 6 3 5 2 3 4 3 3 3 4 - 50160 n q s + 116640 n q s - 104280 n q s + 28560 n q s 3 2 5 3 6 3 7 2 8 2 7 + 6216 n q s - 2856 n q s + 120 n s - 465 n q - 17280 n q s 2 6 2 2 5 3 2 4 4 2 3 5 + 75240 n q s - 116640 n q s + 78210 n q s - 17136 n q s 2 2 6 2 7 2 8 9 8 - 3108 n q s + 1224 n q s - 45 n s - 1390 n q + 930 n q s 7 2 6 3 5 4 4 5 + 17280 n q s - 50160 n q s + 58320 n q s - 31284 n q s 3 6 2 7 8 9 10 9 + 5712 n q s + 888 n q s - 306 n q s + 10 n s - 361 q + 1390 q s 8 2 7 3 6 4 5 5 4 6 - 465 q s - 5760 q s + 12540 q s - 11664 q s + 5214 q s 3 7 2 8 9 10 9 8 8 - 816 q s - 111 q s + 34 q s - s + 4 n - 24 n q - 36 n s 7 2 7 7 2 6 3 6 2 - 786 n q + 192 n q s + 144 n s - 3214 n q + 5502 n q s 6 2 6 3 5 4 5 3 5 2 2 - 672 n q s - 336 n s - 3876 n q + 19284 n q s - 16506 n q s 5 3 5 4 4 5 4 4 4 3 2 + 1344 n q s + 504 n s + 2460 n q + 19380 n q s - 48210 n q s 4 2 3 4 4 4 5 3 6 3 5 + 27510 n q s - 1680 n q s - 504 n s + 10220 n q - 9840 n q s 3 4 2 3 3 3 3 2 4 3 5 - 38760 n q s + 64280 n q s - 27510 n q s + 1344 n q s 3 6 2 7 2 6 2 5 2 2 4 3 + 336 n s + 9660 n q - 30660 n q s + 14760 n q s + 38760 n q s 2 3 4 2 2 5 2 6 2 7 8 - 48210 n q s + 16506 n q s - 672 n q s - 144 n s + 3870 n q 7 6 2 5 3 4 4 - 19320 n q s + 30660 n q s - 9840 n q s - 19380 n q s 3 5 2 6 7 8 9 8 + 19284 n q s - 5502 n q s + 192 n q s + 36 n s + 550 q - 3870 q s 7 2 6 3 5 4 4 5 3 6 + 9660 q s - 10220 q s + 2460 q s + 3876 q s - 3214 q s 2 7 8 9 8 7 7 6 2 + 786 q s - 24 q s - 4 s + 10 n + 260 n q - 80 n s + 580 n q 6 6 2 5 3 5 2 5 2 - 1820 n q s + 280 n s - 2420 n q - 3480 n q s + 5460 n q s 5 3 4 4 4 3 4 2 2 4 3 - 560 n s - 9790 n q + 12100 n q s + 8700 n q s - 9100 n q s 4 4 3 5 3 4 3 3 2 + 700 n s - 12320 n q + 39160 n q s - 24200 n q s 3 2 3 3 4 3 5 2 6 2 5 - 11600 n q s + 9100 n q s - 560 n s - 6035 n q + 36960 n q s 2 4 2 2 3 3 2 2 4 2 5 - 58740 n q s + 24200 n q s + 8700 n q s - 5460 n q s 2 6 7 6 5 2 4 3 + 280 n s - 430 n q + 12070 n q s - 36960 n q s + 39160 n q s 3 4 2 5 6 7 8 7 - 12100 n q s - 3480 n q s + 1820 n q s - 80 n s + 325 q + 430 q s 6 2 5 3 4 4 3 5 2 6 - 6035 q s + 12320 q s - 9790 q s + 2420 q s + 580 q s 7 8 7 6 6 5 2 - 260 q s + 10 s - 30 n + 174 n q + 210 n s + 2424 n q 5 5 2 4 3 4 2 4 2 - 1044 n q s - 630 n s + 4980 n q - 12120 n q s + 2610 n q s 4 3 3 4 3 3 3 2 2 3 3 + 1050 n s + 1260 n q - 19920 n q s + 24240 n q s - 3480 n q s 3 4 2 5 2 4 2 3 2 2 2 3 - 1050 n s - 4530 n q - 3780 n q s + 29880 n q s - 24240 n q s 2 4 2 5 6 5 4 2 + 2610 n q s + 630 n s - 3880 n q + 9060 n q s + 3780 n q s 3 3 2 4 5 6 7 - 19920 n q s + 12120 n q s - 1044 n q s - 210 n s - 850 q 6 5 2 4 3 3 4 2 5 6 + 3880 q s - 4530 q s - 1260 q s + 4980 q s - 2424 q s + 174 q s 7 6 5 5 4 2 4 + 30 s - 64 n - 684 n q + 384 n s + 150 n q + 3420 n q s 4 2 3 3 3 2 3 2 3 3 - 960 n s + 4760 n q - 600 n q s - 6840 n q s + 1280 n s 2 4 2 3 2 2 2 2 3 2 4 + 6075 n q - 14280 n q s + 900 n q s + 6840 n q s - 960 n s 5 4 3 2 2 3 4 + 2070 n q - 12150 n q s + 14280 n q s - 600 n q s - 3420 n q s 5 6 5 4 2 3 3 2 4 + 384 n s - 39 q - 2070 q s + 6075 q s - 4760 q s + 150 q s 5 6 5 4 4 3 2 + 684 q s - 64 s + 50 n - 794 n q - 250 n s - 2626 n q 3 3 2 2 3 2 2 2 2 + 3176 n q s + 500 n s - 714 n q + 7878 n q s - 4764 n q s 2 3 4 3 2 2 3 - 500 n s + 1614 n q + 1428 n q s - 7878 n q s + 3176 n q s 4 5 4 3 2 2 3 4 + 250 n s + 690 q - 1614 q s - 714 q s + 2626 q s - 794 q s 5 4 3 3 2 2 2 - 50 s + 174 n + 276 n q - 696 n s - 1641 n q - 828 n q s 2 2 3 2 2 3 4 + 1044 n s - 1534 n q + 3282 n q s + 828 n q s - 696 n s - 151 q 3 2 2 3 4 3 2 2 + 1534 q s - 1641 q s - 276 q s + 174 s + 70 n + 780 n q - 210 n s 2 2 3 2 2 3 - 60 n q - 1560 n q s + 210 n s - 290 q + 60 q s + 780 q s - 70 s 2 2 2 - 95 n + 374 n q + 190 n s + 109 q - 374 q s - 95 s - 94 n + 50 q /d \ / 3 7 6 6 + 94 s - 24) |-- A[n + 1](r, s)| / ((q + n - s + 1) (n + n q - n s \ds / / 6 5 5 5 4 4 4 3 + 7 n + 6 n q - 6 n s + 21 n + 15 n q - 15 n s + 35 n + 20 n q 3 3 2 2 2 - 20 n s + 35 n + 15 n q - 15 n s + 21 n + 6 n q - 6 n s + 7 n + q 2 2 2 2 2 - s + 1) (n + 2 n q - 2 n s + q - 2 q s + s + n + q - s) (n + q - s) ) 13 4 12 5 12 4 11 6 11 5 - (15 n q + 165 n q - 195 n q s + 825 n q - 1980 n q s 11 4 2 10 7 10 6 10 5 2 + 1170 n q s + 2475 n q - 9075 n q s + 10890 n q s 10 4 3 9 8 9 7 9 6 2 - 4290 n q s + 4950 n q - 24750 n q s + 45375 n q s 9 5 3 9 4 4 8 9 8 8 - 36300 n q s + 10725 n q s + 6930 n q - 44550 n q s 8 7 2 8 6 3 8 5 4 8 4 5 + 111375 n q s - 136125 n q s + 81675 n q s - 19305 n q s 7 10 7 9 7 8 2 7 7 3 + 6930 n q - 55440 n q s + 178200 n q s - 297000 n q s 7 6 4 7 5 5 7 4 6 6 11 + 272250 n q s - 130680 n q s + 25740 n q s + 4950 n q 6 10 6 9 2 6 8 3 6 7 4 - 48510 n q s + 194040 n q s - 415800 n q s + 519750 n q s 6 6 5 6 5 6 6 4 7 5 12 - 381150 n q s + 152460 n q s - 25740 n q s + 2475 n q 5 11 5 10 2 5 9 3 5 8 4 - 29700 n q s + 145530 n q s - 388080 n q s + 623700 n q s 5 7 5 5 6 6 5 5 7 5 4 8 - 623700 n q s + 381150 n q s - 130680 n q s + 19305 n q s 4 13 4 12 4 11 2 4 10 3 + 825 n q - 12375 n q s + 74250 n q s - 242550 n q s 4 9 4 4 8 5 4 7 6 4 6 7 + 485100 n q s - 623700 n q s + 519750 n q s - 272250 n q s 4 5 8 4 4 9 3 14 3 13 + 81675 n q s - 10725 n q s + 165 n q - 3300 n q s 3 12 2 3 11 3 3 10 4 3 9 5 + 24750 n q s - 99000 n q s + 242550 n q s - 388080 n q s 3 8 6 3 7 7 3 6 8 3 5 9 + 415800 n q s - 297000 n q s + 136125 n q s - 36300 n q s 3 4 10 2 15 2 14 2 13 2 + 4290 n q s + 15 n q - 495 n q s + 4950 n q s 2 12 3 2 11 4 2 10 5 2 9 6 - 24750 n q s + 74250 n q s - 145530 n q s + 194040 n q s 2 8 7 2 7 8 2 6 9 2 5 10 - 178200 n q s + 111375 n q s - 45375 n q s + 10890 n q s 2 4 11 15 14 2 13 3 - 1170 n q s - 30 n q s + 495 n q s - 3300 n q s 12 4 11 5 10 6 9 7 + 12375 n q s - 29700 n q s + 48510 n q s - 55440 n q s 8 8 7 9 6 10 5 11 + 44550 n q s - 24750 n q s + 9075 n q s - 1980 n q s 4 12 15 2 14 3 13 4 12 5 + 195 n q s + 15 q s - 165 q s + 825 q s - 2475 q s 11 6 10 7 9 8 8 9 7 10 + 4950 q s - 6930 q s + 6930 q s - 4950 q s + 2475 q s 6 11 5 12 4 13 13 3 12 4 - 825 q s + 165 q s - 15 q s - 60 n q - 765 n q 12 3 11 5 11 4 11 3 2 + 780 n q s - 4320 n q + 9180 n q s - 4680 n q s 10 6 10 5 10 4 2 10 3 3 - 14325 n q + 47520 n q s - 50490 n q s + 17160 n q s 9 7 9 6 9 5 2 9 4 3 - 31050 n q + 143250 n q s - 237600 n q s + 168300 n q s 9 3 4 8 8 8 7 8 6 2 - 42900 n q s - 46170 n q + 279450 n q s - 644625 n q s 8 5 3 8 4 4 8 3 5 7 9 + 712800 n q s - 378675 n q s + 77220 n q s - 47880 n q 7 8 7 7 2 7 6 3 7 5 4 + 369360 n q s - 1117800 n q s + 1719000 n q s - 1425600 n q s 7 4 5 7 3 6 6 10 6 9 + 605880 n q s - 102960 n q s - 34290 n q + 335160 n q s 6 8 2 6 7 3 6 6 4 - 1292760 n q s + 2608200 n q s - 3008250 n q s 6 5 5 6 4 6 6 3 7 5 11 + 1995840 n q s - 706860 n q s + 102960 n q s - 16200 n q 5 10 5 9 2 5 8 3 5 7 4 + 205740 n q s - 1005480 n q s + 2585520 n q s - 3912300 n q s 5 6 5 5 5 6 5 4 7 5 3 8 + 3609900 n q s - 1995840 n q s + 605880 n q s - 77220 n q s 4 12 4 11 4 10 2 4 9 3 - 4425 n q + 81000 n q s - 514350 n q s + 1675800 n q s 4 8 4 4 7 5 4 6 6 - 3231900 n q s + 3912300 n q s - 3008250 n q s 4 5 7 4 4 8 4 3 9 3 13 + 1425600 n q s - 378675 n q s + 42900 n q s - 360 n q 3 12 3 11 2 3 10 3 3 9 4 + 17700 n q s - 162000 n q s + 685800 n q s - 1675800 n q s 3 8 5 3 7 6 3 6 7 3 5 8 + 2585520 n q s - 2608200 n q s + 1719000 n q s - 712800 n q s 3 4 9 3 3 10 2 14 2 13 + 168300 n q s - 17160 n q s + 135 n q + 1080 n q s 2 12 2 2 11 3 2 10 4 2 9 5 - 26550 n q s + 162000 n q s - 514350 n q s + 1005480 n q s 2 8 6 2 7 7 2 6 8 2 5 9 - 1292760 n q s + 1117800 n q s - 644625 n q s + 237600 n q s 2 4 10 2 3 11 15 14 - 50490 n q s + 4680 n q s + 30 n q - 270 n q s 13 2 12 3 11 4 10 5 - 1080 n q s + 17700 n q s - 81000 n q s + 205740 n q s 9 6 8 7 7 8 6 9 - 335160 n q s + 369360 n q s - 279450 n q s + 143250 n q s 5 10 4 11 3 12 15 14 2 - 47520 n q s + 9180 n q s - 780 n q s - 30 q s + 135 q s 13 3 12 4 11 5 10 6 9 7 + 360 q s - 4425 q s + 16200 q s - 34290 q s + 47880 q s 8 8 7 9 6 10 5 11 4 12 - 46170 q s + 31050 q s - 14325 q s + 4320 q s - 765 q s 3 13 13 2 12 3 12 2 11 4 + 60 q s + 105 n q + 1505 n q - 1365 n q s + 9285 n q 11 3 11 2 2 10 5 10 4 - 18060 n q s + 8190 n q s + 32805 n q - 102135 n q s 10 3 2 10 2 3 9 6 9 5 + 99330 n q s - 30030 n q s + 73785 n q - 328050 n q s 9 4 2 9 3 3 9 2 4 8 7 + 510675 n q s - 331100 n q s + 75075 n q s + 110025 n q 8 6 8 5 2 8 4 3 8 3 4 - 664065 n q s + 1476225 n q s - 1532025 n q s + 744975 n q s 8 2 5 7 8 7 7 7 6 2 - 135135 n q s + 108270 n q - 880200 n q s + 2656260 n q s 7 5 3 7 4 4 7 3 5 7 2 6 - 3936600 n q s + 3064050 n q s - 1191960 n q s + 180180 n q s 6 9 6 8 6 7 2 6 6 3 + 65310 n q - 757890 n q s + 3080700 n q s - 6197940 n q s 6 5 4 6 4 5 6 3 6 6 2 7 + 6889050 n q s - 4289670 n q s + 1390620 n q s - 180180 n q s 5 10 5 9 5 8 2 5 7 3 + 16695 n q - 391860 n q s + 2273670 n q s - 6161400 n q s 5 6 4 5 5 5 5 4 6 + 9296910 n q s - 8266860 n q s + 4289670 n q s 5 3 7 5 2 8 4 11 4 10 - 1191960 n q s + 135135 n q s - 6465 n q - 83475 n q s 4 9 2 4 8 3 4 7 4 4 6 5 + 979650 n q s - 3789450 n q s + 7701750 n q s - 9296910 n q s 4 5 6 4 4 7 4 3 8 4 2 9 + 6889050 n q s - 3064050 n q s + 744975 n q s - 75075 n q s 3 12 3 11 3 10 2 3 9 3 - 6955 n q + 25860 n q s + 166950 n q s - 1306200 n q s 3 8 4 3 7 5 3 6 6 + 3789450 n q s - 6161400 n q s + 6197940 n q s 3 5 7 3 4 8 3 3 9 3 2 10 - 3936600 n q s + 1532025 n q s - 331100 n q s + 30030 n q s 2 13 2 12 2 11 2 2 10 3 - 2235 n q + 20865 n q s - 38790 n q s - 166950 n q s 2 9 4 2 8 5 2 7 6 2 6 7 + 979650 n q s - 2273670 n q s + 3080700 n q s - 2656260 n q s 2 5 8 2 4 9 2 3 10 2 2 11 + 1476225 n q s - 510675 n q s + 99330 n q s - 8190 n q s 14 13 12 2 11 3 - 225 n q + 4470 n q s - 20865 n q s + 25860 n q s 10 4 9 5 8 6 7 7 + 83475 n q s - 391860 n q s + 757890 n q s - 880200 n q s 6 8 5 9 4 10 3 11 + 664065 n q s - 328050 n q s + 102135 n q s - 18060 n q s 2 12 15 14 13 2 12 3 + 1365 n q s + 15 q + 225 q s - 2235 q s + 6955 q s 11 4 10 5 9 6 8 7 7 8 - 6465 q s - 16695 q s + 65310 q s - 108270 q s + 110025 q s 6 9 5 10 4 11 3 12 2 13 - 73785 q s + 32805 q s - 9285 q s + 1505 q s - 105 q s 13 12 2 12 11 3 11 2 - 90 n q - 1515 n q + 1170 n q s - 10020 n q + 18180 n q s 11 2 10 4 10 3 10 2 2 - 7020 n q s - 35505 n q + 110220 n q s - 99990 n q s 10 3 9 5 9 4 9 3 2 + 25740 n q s - 73950 n q + 355050 n q s - 551100 n q s 9 2 3 9 4 8 6 8 5 + 333300 n q s - 64350 n q s - 87345 n q + 665550 n q s 8 4 2 8 3 3 8 2 4 8 5 - 1597725 n q s + 1653300 n q s - 749925 n q s + 115830 n q s 7 7 7 6 7 5 2 7 4 3 - 36000 n q + 698760 n q s - 2662200 n q s + 4260600 n q s 7 3 4 7 2 5 7 6 6 8 - 3306600 n q s + 1199880 n q s - 154440 n q s + 54090 n q 6 7 6 6 2 6 5 3 6 4 4 + 252000 n q s - 2445660 n q s + 6211800 n q s - 7456050 n q s 6 3 5 6 2 6 6 7 5 9 + 4629240 n q s - 1399860 n q s + 154440 n q s + 104850 n q 5 8 5 7 2 5 6 3 5 5 4 - 324540 n q s - 756000 n q s + 4891320 n q s - 9317700 n q s 5 4 5 5 3 6 5 2 7 5 8 + 8947260 n q s - 4629240 n q s + 1199880 n q s - 115830 n q s 4 10 4 9 4 8 2 4 7 3 + 84375 n q - 524250 n q s + 811350 n q s + 1260000 n q s 4 6 4 4 5 5 4 4 6 - 6114150 n q s + 9317700 n q s - 7456050 n q s 4 3 7 4 2 8 4 9 3 11 + 3306600 n q s - 749925 n q s + 64350 n q s + 36420 n q 3 10 3 9 2 3 8 3 3 7 4 - 337500 n q s + 1048500 n q s - 1081800 n q s - 1260000 n q s 3 6 5 3 5 6 3 4 7 + 4891320 n q s - 6211800 n q s + 4260600 n q s 3 3 8 3 2 9 3 10 2 12 - 1653300 n q s + 333300 n q s - 25740 n q s + 7215 n q 2 11 2 10 2 2 9 3 2 8 4 - 109260 n q s + 506250 n q s - 1048500 n q s + 811350 n q s 2 7 5 2 6 6 2 5 7 2 4 8 + 756000 n q s - 2445660 n q s + 2662200 n q s - 1597725 n q s 2 3 9 2 2 10 2 11 13 + 551100 n q s - 99990 n q s + 7020 n q s - 90 n q 12 11 2 10 3 9 4 - 14430 n q s + 109260 n q s - 337500 n q s + 524250 n q s 8 5 7 6 6 7 5 8 - 324540 n q s - 252000 n q s + 698760 n q s - 665550 n q s 4 9 3 10 2 11 12 + 355050 n q s - 110220 n q s + 18180 n q s - 1170 n q s 14 13 12 2 11 3 10 4 - 195 q + 90 q s + 7215 q s - 36420 q s + 84375 q s 9 5 8 6 7 7 6 8 5 9 - 104850 q s + 54090 q s + 36000 q s - 87345 q s + 73950 q s 4 10 3 11 2 12 13 13 - 35505 q s + 10020 q s - 1515 q s + 90 q s + 31 n 12 12 11 2 11 11 2 + 733 n q - 403 n s + 4983 n q - 8796 n q s + 2418 n s 10 3 10 2 10 2 10 3 + 13641 n q - 54813 n q s + 48378 n q s - 8866 n s 9 4 9 3 9 2 2 9 3 + 4890 n q - 136410 n q s + 274065 n q s - 161260 n q s 9 4 8 5 8 4 8 3 2 + 22165 n s - 70254 n q - 44010 n q s + 613845 n q s 8 2 3 8 4 8 5 7 6 - 822195 n q s + 362835 n q s - 39897 n s - 218322 n q 7 5 7 4 2 7 3 3 7 2 4 + 562032 n q s + 176040 n q s - 1636920 n q s + 1644390 n q s 7 5 7 6 6 7 6 6 - 580536 n q s + 53196 n s - 336942 n q + 1528254 n q s 6 5 2 6 4 3 6 3 4 6 2 5 - 1967112 n q s - 410760 n q s + 2864610 n q s - 2302146 n q s 6 6 6 7 5 8 5 7 + 677292 n q s - 53196 n s - 311229 n q + 2021652 n q s 5 6 2 5 5 3 5 4 4 5 3 5 - 4584762 n q s + 3934224 n q s + 616140 n q s - 3437532 n q s 5 2 6 5 7 5 8 4 9 + 2302146 n q s - 580536 n q s + 39897 n s - 170255 n q 4 8 4 7 2 4 6 3 4 5 4 + 1556145 n q s - 5054130 n q s + 7641270 n q s - 4917780 n q s 4 4 5 4 3 6 4 2 7 4 8 - 616140 n q s + 2864610 n q s - 1644390 n q s + 362835 n q s 4 9 3 10 3 9 3 8 2 - 22165 n s - 44165 n q + 681020 n q s - 3112290 n q s 3 7 3 3 6 4 3 5 5 3 4 6 + 6738840 n q s - 7641270 n q s + 3934224 n q s + 410760 n q s 3 3 7 3 2 8 3 9 3 10 - 1636920 n q s + 822195 n q s - 161260 n q s + 8866 n s 2 11 2 10 2 9 2 2 8 3 + 3525 n q + 132495 n q s - 1021530 n q s + 3112290 n q s 2 7 4 2 6 5 2 5 6 2 4 7 - 5054130 n q s + 4584762 n q s - 1967112 n q s - 176040 n q s 2 3 8 2 2 9 2 10 2 11 + 613845 n q s - 274065 n q s + 48378 n q s - 2418 n s 12 11 10 2 9 3 + 5220 n q - 7050 n q s - 132495 n q s + 681020 n q s 8 4 7 5 6 6 5 7 - 1556145 n q s + 2021652 n q s - 1528254 n q s + 562032 n q s 4 8 3 9 2 10 11 + 44010 n q s - 136410 n q s + 54813 n q s - 8796 n q s 12 13 12 11 2 10 3 + 403 n s + 960 q - 5220 q s + 3525 q s + 44165 q s 9 4 8 5 7 6 6 7 5 8 - 170255 q s + 311229 q s - 336942 q s + 218322 q s - 70254 q s 4 9 3 10 2 11 12 13 12 - 4890 q s + 13641 q s - 4983 q s + 733 q s - 31 s - 119 n 11 11 10 2 10 10 2 - 438 n q + 1428 n s + 5841 n q + 4818 n q s - 7854 n s 9 3 9 2 9 2 9 3 8 4 + 49520 n q - 58410 n q s - 24090 n q s + 26180 n s + 168300 n q 8 3 8 2 2 8 3 8 4 - 445680 n q s + 262845 n q s + 72270 n q s - 58905 n s 7 5 7 4 7 3 2 7 2 3 + 317106 n q - 1346400 n q s + 1782720 n q s - 700920 n q s 7 4 7 5 6 6 6 5 - 144540 n q s + 94248 n s + 348042 n q - 2219742 n q s 6 4 2 6 3 3 6 2 4 6 5 + 4712400 n q s - 4159680 n q s + 1226610 n q s + 202356 n q s 6 6 5 7 5 6 5 5 2 - 109956 n s + 194346 n q - 2088252 n q s + 6659226 n q s 5 4 3 5 3 4 5 2 5 5 6 - 9424800 n q s + 6239520 n q s - 1471932 n q s - 202356 n q s 5 7 4 8 4 7 4 6 2 + 94248 n s - 3915 n q - 971730 n q s + 5220630 n q s 4 5 3 4 4 4 4 3 5 - 11098710 n q s + 11781000 n q s - 6239520 n q s 4 2 6 4 7 4 8 3 9 + 1226610 n q s + 144540 n q s - 58905 n s - 84860 n q 3 8 3 7 2 3 6 3 3 5 4 + 15660 n q s + 1943460 n q s - 6960840 n q s + 11098710 n q s 3 4 5 3 3 6 3 2 7 3 8 - 9424800 n q s + 4159680 n q s - 700920 n q s - 72270 n q s 3 9 2 10 2 9 2 8 2 + 26180 n s - 57795 n q + 254580 n q s - 23490 n q s 2 7 3 2 6 4 2 5 5 - 1943460 n q s + 5220630 n q s - 6659226 n q s 2 4 6 2 3 7 2 2 8 2 9 + 4712400 n q s - 1782720 n q s + 262845 n q s + 24090 n q s 2 10 11 10 9 2 - 7854 n s - 17370 n q + 115590 n q s - 254580 n q s 8 3 7 4 6 5 5 6 + 15660 n q s + 971730 n q s - 2088252 n q s + 2219742 n q s 4 7 3 8 2 9 10 - 1346400 n q s + 445680 n q s - 58410 n q s - 4818 n q s 11 12 11 10 2 9 3 + 1428 n s - 2050 q + 17370 q s - 57795 q s + 84860 q s 8 4 7 5 6 6 5 7 4 8 - 3915 q s - 194346 q s + 348042 q s - 317106 q s + 168300 q s 3 9 2 10 11 12 11 10 - 49520 q s + 5841 q s + 438 q s - 119 s - 309 n - 5769 n q 10 9 2 9 9 2 8 3 + 3399 n s - 32295 n q + 57690 n q s - 16995 n s - 79515 n q 8 2 8 2 8 3 7 4 + 290655 n q s - 259605 n q s + 50985 n s - 71130 n q 7 3 7 2 2 7 3 7 4 + 636120 n q s - 1162620 n q s + 692280 n q s - 101970 n s 6 5 6 4 6 3 2 6 2 3 + 84126 n q + 497910 n q s - 2226420 n q s + 2712780 n q s 6 4 6 5 5 6 5 5 - 1211490 n q s + 142758 n s + 304041 n q - 504756 n q s 5 4 2 5 3 3 5 2 4 5 5 - 1493730 n q s + 4452840 n q s - 4069170 n q s + 1453788 n q s 5 6 4 7 4 6 4 5 2 - 142758 n s + 375165 n q - 1520205 n q s + 1261890 n q s 4 4 3 4 3 4 4 2 5 4 6 + 2489550 n q s - 5566050 n q s + 4069170 n q s - 1211490 n q s 4 7 3 8 3 7 3 6 2 + 101970 n s + 250965 n q - 1500660 n q s + 3040410 n q s 3 5 3 3 4 4 3 3 5 - 1682520 n q s - 2489550 n q s + 4452840 n q s 3 2 6 3 7 3 8 2 9 - 2712780 n q s + 692280 n q s - 50985 n s + 93105 n q 2 8 2 7 2 2 6 3 2 5 4 - 752895 n q s + 2250990 n q s - 3040410 n q s + 1261890 n q s 2 4 5 2 3 6 2 2 7 2 8 + 1493730 n q s - 2226420 n q s + 1162620 n q s - 259605 n q s 2 9 10 9 8 2 + 16995 n s + 16680 n q - 186210 n q s + 752895 n q s 7 3 6 4 5 5 4 6 - 1500660 n q s + 1520205 n q s - 504756 n q s - 497910 n q s 3 7 2 8 9 10 11 + 636120 n q s - 290655 n q s + 57690 n q s - 3399 n s + 840 q 10 9 2 8 3 7 4 6 5 - 16680 q s + 93105 q s - 250965 q s + 375165 q s - 304041 q s 5 6 4 7 3 8 2 9 10 + 84126 q s + 71130 q s - 79515 q s + 32295 q s - 5769 q s 11 10 9 9 8 2 8 + 309 s + 811 n + 2110 n q - 8110 n s - 20835 n q - 18990 n q s 8 2 7 3 7 2 7 2 + 36495 n s - 130800 n q + 166680 n q s + 75960 n q s 7 3 6 4 6 3 6 2 2 - 97320 n s - 325860 n q + 915600 n q s - 583380 n q s 6 3 6 4 5 5 5 4 - 177240 n q s + 170310 n s - 437994 n q + 1955160 n q s 5 3 2 5 2 3 5 4 5 5 - 2746800 n q s + 1166760 n q s + 265860 n q s - 204372 n s 4 6 4 5 4 4 2 4 3 3 - 326265 n q + 2189970 n q s - 4887900 n q s + 4578000 n q s 4 2 4 4 5 4 6 3 7 - 1458450 n q s - 265860 n q s + 170310 n s - 111000 n q 3 6 3 5 2 3 4 3 3 3 4 + 1305060 n q s - 4379940 n q s + 6517200 n q s - 4578000 n q s 3 2 5 3 6 3 7 2 8 + 1166760 n q s + 177240 n q s - 97320 n s + 8595 n q 2 7 2 6 2 2 5 3 2 4 4 + 333000 n q s - 1957590 n q s + 4379940 n q s - 4887900 n q s 2 3 5 2 2 6 2 7 2 8 + 2746800 n q s - 583380 n q s - 75960 n q s + 36495 n s 9 8 7 2 6 3 + 17980 n q - 17190 n q s - 333000 n q s + 1305060 n q s 5 4 4 5 3 6 2 7 - 2189970 n q s + 1955160 n q s - 915600 n q s + 166680 n q s 8 9 10 9 8 2 + 18990 n q s - 8110 n s + 3850 q - 17980 q s + 8595 q s 7 3 6 4 5 5 4 6 3 7 + 111000 q s - 326265 q s + 437994 q s - 325860 q s + 130800 q s 2 8 9 10 9 8 8 - 20835 q s - 2110 q s + 811 s + 1880 n + 19404 n q - 16920 n s 7 2 7 7 2 6 3 + 69522 n q - 155232 n q s + 67680 n s + 105782 n q 6 2 6 2 6 3 5 4 - 486654 n q s + 543312 n q s - 157920 n s + 27579 n q 5 3 5 2 2 5 3 5 4 - 634692 n q s + 1459962 n q s - 1086624 n q s + 236880 n s 4 5 4 4 4 3 2 4 2 3 - 135795 n q - 137895 n q s + 1586730 n q s - 2433270 n q s 4 4 4 5 3 6 3 5 + 1358280 n q s - 236880 n s - 208025 n q + 543180 n q s 3 4 2 3 3 3 3 2 4 3 5 + 275790 n q s - 2115640 n q s + 2433270 n q s - 1086624 n q s 3 6 2 7 2 6 2 5 2 + 157920 n s - 135915 n q + 624075 n q s - 814770 n q s 2 4 3 2 3 4 2 2 5 2 6 - 275790 n q s + 1586730 n q s - 1459962 n q s + 543312 n q s 2 7 8 7 6 2 - 67680 n s - 42480 n q + 271830 n q s - 624075 n q s 5 3 4 4 3 5 2 6 + 543180 n q s + 137895 n q s - 634692 n q s + 486654 n q s 7 8 9 8 7 2 - 155232 n q s + 16920 n s - 5000 q + 42480 q s - 135915 q s 6 3 5 4 4 5 3 6 2 7 + 208025 q s - 135795 q s - 27579 q s + 105782 q s - 69522 q s 8 9 8 7 7 6 2 + 19404 q s - 1880 s - 798 n + 6540 n q + 6384 n s + 59094 n q 6 6 2 5 3 5 2 - 45780 n q s - 22344 n s + 169356 n q - 354564 n q s 5 2 5 3 4 4 4 3 + 137340 n q s + 44688 n s + 242205 n q - 846780 n q s 4 2 2 4 3 4 4 3 5 + 886410 n q s - 228900 n q s - 55860 n s + 184326 n q 3 4 3 3 2 3 2 3 3 4 - 968820 n q s + 1693560 n q s - 1181880 n q s + 228900 n q s 3 5 2 6 2 5 2 4 2 + 44688 n s + 66693 n q - 552978 n q s + 1453230 n q s 2 3 3 2 2 4 2 5 2 6 - 1693560 n q s + 886410 n q s - 137340 n q s - 22344 n s 7 6 5 2 4 3 + 4848 n q - 133386 n q s + 552978 n q s - 968820 n q s 3 4 2 5 6 7 8 + 846780 n q s - 354564 n q s + 45780 n q s + 6384 n s - 2124 q 7 6 2 5 3 4 4 3 5 - 4848 q s + 66693 q s - 184326 q s + 242205 q s - 169356 q s 2 6 7 8 7 6 6 + 59094 q s - 6540 q s - 798 s - 4058 n - 20282 n q + 28406 n s 5 2 5 5 2 4 3 4 2 - 35529 n q + 121692 n q s - 85218 n s - 11545 n q + 177645 n q s 4 2 4 3 3 4 3 3 - 304230 n q s + 142030 n s + 43565 n q + 46180 n q s 3 2 2 3 3 3 4 2 5 - 355290 n q s + 405640 n q s - 142030 n s + 63021 n q 2 4 2 3 2 2 2 3 2 4 - 130695 n q s - 69270 n q s + 355290 n q s - 304230 n q s 2 5 6 5 4 2 + 85218 n s + 33552 n q - 126042 n q s + 130695 n q s 3 3 2 4 5 6 7 + 46180 n q s - 177645 n q s + 121692 n q s - 28406 n s + 6336 q 6 5 2 4 3 3 4 2 5 - 33552 q s + 63021 q s - 43565 q s - 11545 q s + 35529 q s 6 7 6 5 5 4 2 - 20282 q s + 4058 s - 2858 n - 16374 n q + 17148 n s - 41925 n q 4 4 2 3 3 3 2 + 81870 n q s - 42870 n s - 58540 n q + 167700 n q s 3 2 3 3 2 4 2 3 - 163740 n q s + 57160 n s - 43275 n q + 175620 n q s 2 2 2 2 3 2 4 5 - 251550 n q s + 163740 n q s - 42870 n s - 14064 n q 4 3 2 2 3 4 + 86550 n q s - 175620 n q s + 167700 n q s - 81870 n q s 5 6 5 4 2 3 3 + 17148 n s - 944 q + 14064 q s - 43275 q s + 58540 q s 2 4 5 6 5 4 4 - 41925 q s + 16374 q s - 2858 s - 513 n - 1395 n q + 2565 n s 3 2 3 3 2 2 3 2 2 - 2385 n q + 5580 n q s - 5130 n s - 6135 n q + 7155 n q s 2 2 2 3 4 3 2 2 - 8370 n q s + 5130 n s - 7740 n q + 12270 n q s - 7155 n q s 3 4 5 4 3 2 2 3 + 5580 n q s - 2565 n s - 2964 q + 7740 q s - 6135 q s + 2385 q s 4 5 4 3 3 2 2 2 - 1395 q s + 513 s - 195 n - 6 n q + 780 n s + 2817 n q + 18 n q s 2 2 3 2 2 3 4 - 1170 n s + 4352 n q - 5634 n q s - 18 n q s + 780 n s + 1364 q 3 2 2 3 4 3 2 2 - 4352 q s + 2817 q s + 6 q s - 195 s - 129 n - 1053 n q + 387 n s 2 2 3 2 2 - 1329 n q + 2106 n q s - 387 n s + 75 q + 1329 q s - 1053 q s 3 2 2 2 + 129 s + 111 n + 66 n q - 222 n s - 405 q - 66 q s + 111 s + 26 n / 2 \ |d | / 8 7 7 + 170 q - 26 s - 24) |--- A[n + 1](r, s)| / ((n + 2 n q - 2 n s | 2 | / \ds / 6 2 6 6 2 7 6 6 5 2 + n q - 2 n q s + n s + 7 n + 13 n q - 13 n s + 6 n q 5 5 2 6 5 5 4 2 4 - 12 n q s + 6 n s + 21 n + 36 n q - 36 n s + 15 n q - 30 n q s 4 2 5 4 4 3 2 3 3 2 + 15 n s + 35 n + 55 n q - 55 n s + 20 n q - 40 n q s + 20 n s 4 3 3 2 2 2 2 2 3 + 35 n + 50 n q - 50 n s + 15 n q - 30 n q s + 15 n s + 21 n 2 2 2 2 2 + 27 n q - 27 n s + 6 n q - 12 n q s + 6 n s + 7 n + 8 n q - 8 n s 2 2 2 3 2 2 + q - 2 q s + s + n + q - s) (q + n - s + 1) (n + 3 n q - 3 n s 2 2 3 2 2 3 2 + 3 n q - 6 n q s + 3 n s + q - 3 q s + 3 q s - s - n - q + s) %2) 11 3 10 4 10 3 9 5 9 4 - 2 (10 n q + 110 n q - 110 n q s + 550 n q - 1100 n q s 9 3 2 8 6 8 5 8 4 2 8 3 3 + 550 n q s + 1650 n q - 4950 n q s + 4950 n q s - 1650 n q s 7 7 7 6 7 5 2 7 4 3 + 3300 n q - 13200 n q s + 19800 n q s - 13200 n q s 7 3 4 6 8 6 7 6 6 2 + 3300 n q s + 4620 n q - 23100 n q s + 46200 n q s 6 5 3 6 4 4 6 3 5 5 9 - 46200 n q s + 23100 n q s - 4620 n q s + 4620 n q 5 8 5 7 2 5 6 3 5 5 4 - 27720 n q s + 69300 n q s - 92400 n q s + 69300 n q s 5 4 5 5 3 6 4 10 4 9 - 27720 n q s + 4620 n q s + 3300 n q - 23100 n q s 4 8 2 4 7 3 4 6 4 4 5 5 + 69300 n q s - 115500 n q s + 115500 n q s - 69300 n q s 4 4 6 4 3 7 3 11 3 10 + 23100 n q s - 3300 n q s + 1650 n q - 13200 n q s 3 9 2 3 8 3 3 7 4 3 6 5 + 46200 n q s - 92400 n q s + 115500 n q s - 92400 n q s 3 5 6 3 4 7 3 3 8 2 12 + 46200 n q s - 13200 n q s + 1650 n q s + 550 n q 2 11 2 10 2 2 9 3 2 8 4 - 4950 n q s + 19800 n q s - 46200 n q s + 69300 n q s 2 7 5 2 6 6 2 5 7 2 4 8 - 69300 n q s + 46200 n q s - 19800 n q s + 4950 n q s 2 3 9 13 12 11 2 10 3 - 550 n q s + 110 n q - 1100 n q s + 4950 n q s - 13200 n q s 9 4 8 5 7 6 6 7 + 23100 n q s - 27720 n q s + 23100 n q s - 13200 n q s 5 8 4 9 3 10 14 13 + 4950 n q s - 1100 n q s + 110 n q s + 10 q - 110 q s 12 2 11 3 10 4 9 5 8 6 + 550 q s - 1650 q s + 3300 q s - 4620 q s + 4620 q s 7 7 6 8 5 9 4 10 3 11 11 2 - 3300 q s + 1650 q s - 550 q s + 110 q s - 10 q s - 45 n q 10 3 10 2 9 4 9 3 9 2 2 - 610 n q + 495 n q s - 3625 n q + 6100 n q s - 2475 n q s 8 5 8 4 8 3 2 8 2 3 - 12600 n q + 32625 n q s - 27450 n q s + 7425 n q s 7 6 7 5 7 4 2 7 3 3 - 28650 n q + 100800 n q s - 130500 n q s + 73200 n q s 7 2 4 6 7 6 6 6 5 2 - 14850 n q s - 44940 n q + 200550 n q s - 352800 n q s 6 4 3 6 3 4 6 2 5 5 8 + 304500 n q s - 128100 n q s + 20790 n q s - 49770 n q 5 7 5 6 2 5 5 3 5 4 4 + 269640 n q s - 601650 n q s + 705600 n q s - 456750 n q s 5 3 5 5 2 6 4 9 4 8 + 153720 n q s - 20790 n q s - 39000 n q + 248850 n q s 4 7 2 4 6 3 4 5 4 4 4 5 - 674100 n q s + 1002750 n q s - 882000 n q s + 456750 n q s 4 3 6 4 2 7 3 10 3 9 - 128100 n q s + 14850 n q s - 21225 n q + 156000 n q s 3 8 2 3 7 3 3 6 4 3 5 5 - 497700 n q s + 898800 n q s - 1002750 n q s + 705600 n q s 3 4 6 3 3 7 3 2 8 2 11 - 304500 n q s + 73200 n q s - 7425 n q s - 7650 n q 2 10 2 9 2 2 8 3 2 7 4 + 63675 n q s - 234000 n q s + 497700 n q s - 674100 n q s 2 6 5 2 5 6 2 4 7 2 3 8 + 601650 n q s - 352800 n q s + 130500 n q s - 27450 n q s 2 2 9 12 11 10 2 + 2475 n q s - 1645 n q + 15300 n q s - 63675 n q s 9 3 8 4 7 5 6 6 + 156000 n q s - 248850 n q s + 269640 n q s - 200550 n q s 5 7 4 8 3 9 2 10 13 + 100800 n q s - 32625 n q s + 6100 n q s - 495 n q s - 160 q 12 11 2 10 3 9 4 8 5 + 1645 q s - 7650 q s + 21225 q s - 39000 q s + 49770 q s 7 6 6 7 5 8 4 9 3 10 - 44940 q s + 28650 q s - 12600 q s + 3625 q s - 610 q s 2 11 11 10 2 10 9 3 + 45 q s + 75 n q + 1290 n q - 825 n q s + 9270 n q 9 2 9 2 8 4 8 3 - 12900 n q s + 4125 n q s + 37755 n q - 83430 n q s 8 2 2 8 3 7 5 7 4 + 58050 n q s - 12375 n q s + 98370 n q - 302040 n q s 7 3 2 7 2 3 7 4 6 6 + 333720 n q s - 154800 n q s + 24750 n q s + 173880 n q 6 5 6 4 2 6 3 3 6 2 4 - 688590 n q s + 1057140 n q s - 778680 n q s + 270900 n q s 6 5 5 7 5 6 5 5 2 - 34650 n q s + 214200 n q - 1043280 n q s + 2065770 n q s 5 4 3 5 3 4 5 2 5 5 6 - 2114280 n q s + 1168020 n q s - 325080 n q s + 34650 n q s 4 8 4 7 4 6 2 4 5 3 + 184770 n q - 1071000 n q s + 2608200 n q s - 3442950 n q s 4 4 4 4 3 5 4 2 6 4 7 + 2642850 n q s - 1168020 n q s + 270900 n q s - 24750 n q s 3 9 3 8 3 7 2 3 6 3 + 109755 n q - 739080 n q s + 2142000 n q s - 3477600 n q s 3 5 4 3 4 5 3 3 6 3 2 7 + 3442950 n q s - 2114280 n q s + 778680 n q s - 154800 n q s 3 8 2 10 2 9 2 8 2 + 12375 n q s + 42870 n q - 329265 n q s + 1108620 n q s 2 7 3 2 6 4 2 5 5 - 2142000 n q s + 2608200 n q s - 2065770 n q s 2 4 6 2 3 7 2 2 8 2 9 + 1057140 n q s - 333720 n q s + 58050 n q s - 4125 n q s 11 10 9 2 8 3 + 9930 n q - 85740 n q s + 329265 n q s - 739080 n q s 7 4 6 5 5 6 4 7 + 1071000 n q s - 1043280 n q s + 688590 n q s - 302040 n q s 3 8 2 9 10 12 11 + 83430 n q s - 12900 n q s + 825 n q s + 1035 q - 9930 q s 10 2 9 3 8 4 7 5 6 6 + 42870 q s - 109755 q s + 184770 q s - 214200 q s + 173880 q s 5 7 4 8 3 9 2 10 11 11 - 98370 q s + 37755 q s - 9270 q s + 1290 q s - 75 q s - 45 n 10 10 9 2 9 9 2 - 1200 n q + 495 n s - 11175 n q + 12000 n q s - 2475 n s 8 3 8 2 8 2 8 3 7 4 - 54960 n q + 100575 n q s - 54000 n q s + 7425 n s - 166530 n q 7 3 7 2 2 7 3 7 4 + 439680 n q s - 402300 n q s + 144000 n q s - 14850 n s 6 5 6 4 6 3 2 6 2 3 - 334320 n q + 1165710 n q s - 1538880 n q s + 938700 n q s 6 4 6 5 5 6 5 5 - 252000 n q s + 20790 n s - 460110 n q + 2005920 n q s 5 4 2 5 3 3 5 2 4 5 5 - 3497130 n q s + 3077760 n q s - 1408050 n q s + 302400 n q s 5 6 4 7 4 6 4 5 2 - 20790 n s - 438000 n q + 2300550 n q s - 5014800 n q s 4 4 3 4 3 4 4 2 5 4 6 + 5828550 n q s - 3847200 n q s + 1408050 n q s - 252000 n q s 4 7 3 8 3 7 3 6 2 + 14850 n s - 284385 n q + 1752000 n q s - 4601100 n q s 3 5 3 3 4 4 3 3 5 3 2 6 + 6686400 n q s - 5828550 n q s + 3077760 n q s - 938700 n q s 3 7 3 8 2 9 2 8 + 144000 n q s - 7425 n s - 120480 n q + 853155 n q s 2 7 2 2 6 3 2 5 4 - 2628000 n q s + 4601100 n q s - 5014800 n q s 2 4 5 2 3 6 2 2 7 2 8 + 3497130 n q s - 1538880 n q s + 402300 n q s - 54000 n q s 2 9 10 9 8 2 + 2475 n s - 30075 n q + 240960 n q s - 853155 n q s 7 3 6 4 5 5 4 6 + 1752000 n q s - 2300550 n q s + 2005920 n q s - 1165710 n q s 3 7 2 8 9 10 11 + 439680 n q s - 100575 n q s + 12000 n q s - 495 n s - 3360 q 10 9 2 8 3 7 4 6 5 + 30075 q s - 120480 q s + 284385 q s - 438000 q s + 460110 q s 5 6 4 7 3 8 2 9 10 - 334320 q s + 166530 q s - 54960 q s + 11175 q s - 1200 q s 11 10 9 9 8 2 8 + 45 s + 388 n + 5944 n q - 3880 n s + 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856380 n q s + 1955040 n q s 2 4 4 2 3 5 2 2 6 2 7 - 1469550 n q s - 557760 n q s + 1464120 n q s - 775440 n q s 2 8 9 8 7 2 6 3 + 132570 n s + 4140 n q - 19920 n q s - 97440 n q s + 570920 n q s 5 4 4 5 3 6 2 7 - 977520 n q s + 587820 n q s + 185920 n q s - 418320 n q s 8 9 10 9 8 2 + 193860 n q s - 29460 n s - 240 q - 4140 q s + 9960 q s 7 3 6 4 5 5 4 6 3 7 + 32480 q s - 142730 q s + 195504 q s - 97970 q s - 26560 q s 2 8 9 10 9 8 8 + 52290 q s - 21540 q s + 2946 s - 210 n + 18090 n q + 1890 n s 7 2 7 7 2 6 3 + 110850 n q - 144720 n q s - 7560 n s + 254030 n q 6 2 6 2 6 3 5 4 - 775950 n q s + 506520 n q s + 17640 n s + 261885 n q 5 3 5 2 2 5 3 5 4 - 1524180 n q s + 2327850 n q s - 1013040 n q s - 26460 n s 4 5 4 4 4 3 2 4 2 3 + 81915 n q - 1309425 n q s + 3810450 n q s - 3879750 n q s 4 4 4 5 3 6 3 5 + 1266300 n q s + 26460 n s - 60715 n q - 327660 n q s 3 4 2 3 3 3 3 2 4 3 5 + 2618850 n q s - 5080600 n q s + 3879750 n q s - 1013040 n q s 3 6 2 7 2 6 2 5 2 - 17640 n s - 51465 n q + 182145 n q s + 491490 n q s 2 4 3 2 3 4 2 2 5 2 6 - 2618850 n q s + 3810450 n q s - 2327850 n q s + 506520 n q s 2 7 8 7 6 2 5 3 + 7560 n s - 7710 n q + 102930 n q s - 182145 n q s - 327660 n q s 4 4 3 5 2 6 7 + 1309425 n q s - 1524180 n q s + 775950 n q s - 144720 n q s 8 9 8 7 2 6 3 - 1890 n s + 1530 q + 7710 q s - 51465 q s + 60715 q s 5 4 4 5 3 6 2 7 8 + 81915 q s - 261885 q s + 254030 q s - 110850 q s + 18090 q s 9 8 7 7 6 2 6 + 210 s - 9840 n - 55500 n q + 78720 n s - 88920 n q + 388500 n q s 6 2 5 3 5 2 5 2 - 275520 n s + 24180 n q + 533520 n q s - 1165500 n q s 5 3 4 4 4 3 4 2 2 + 551040 n s + 207900 n q - 120900 n q s - 1333800 n q s 4 3 4 4 3 5 3 4 + 1942500 n q s - 688800 n s + 210510 n q - 831600 n q s 3 3 2 3 2 3 3 4 3 5 + 241800 n q s + 1778400 n q s - 1942500 n q s + 551040 n s 2 6 2 5 2 4 2 2 3 3 + 69720 n q - 631530 n q s + 1247400 n q s - 241800 n q s 2 2 4 2 5 2 6 7 - 1333800 n q s + 1165500 n q s - 275520 n s - 5130 n q 6 5 2 4 3 3 4 - 139440 n q s + 631530 n q s - 831600 n q s + 120900 n q s 2 5 6 7 8 7 + 533520 n q s - 388500 n q s + 78720 n s - 4800 q + 5130 q s 6 2 5 3 4 4 3 5 2 6 + 69720 q s - 210510 q s + 207900 q s - 24180 q s - 88920 q s 7 8 7 6 6 5 2 + 55500 q s - 9840 s - 1710 n - 48186 n q + 11970 n s - 185751 n q 5 5 2 4 3 4 2 + 289116 n q s - 35910 n s - 264835 n q + 928755 n q s 4 2 4 3 3 4 3 3 - 722790 n q s + 59850 n s - 129925 n q + 1059340 n q s 3 2 2 3 3 3 4 2 5 - 1857510 n q s + 963720 n q s - 59850 n s + 28785 n q 2 4 2 3 2 2 2 3 2 4 + 389775 n q s - 1589010 n q s + 1857510 n q s - 722790 n q s 2 5 6 5 4 2 + 35910 n s + 40010 n q - 57570 n q s - 389775 n q s 3 3 2 4 5 6 7 + 1059340 n q s - 928755 n q s + 289116 n q s - 11970 n s + 6860 q 6 5 2 4 3 3 4 2 5 - 40010 q s + 28785 q s + 129925 q s - 264835 q s + 185751 q s 6 7 6 5 5 4 2 - 48186 q s + 1710 s + 15372 n + 53676 n q - 92232 n s + 19080 n q 4 4 2 3 3 3 2 - 268380 n q s + 230580 n s - 108620 n q - 76320 n q s 3 2 3 3 2 4 2 3 + 536760 n q s - 307440 n s - 134610 n q + 325860 n q s 2 2 2 2 3 2 4 5 + 114480 n q s - 536760 n q s + 230580 n s - 45564 n q 4 3 2 2 3 4 + 269220 n q s - 325860 n q s - 76320 n q s + 268380 n q s 5 6 5 4 2 3 3 - 92232 n s - 494 q + 45564 q s - 134610 q s + 108620 q s 2 4 5 6 5 4 4 + 19080 q s - 53676 q s + 15372 s + 7077 n + 59175 n q - 35385 n s 3 2 3 3 2 2 3 + 117465 n q - 236700 n q s + 70770 n s + 68715 n q 2 2 2 2 2 3 4 - 352395 n q s + 355050 n q s - 70770 n s - 7710 n q 3 2 2 3 4 5 - 137430 n q s + 352395 n q s - 236700 n q s + 35385 n s - 10194 q 4 3 2 2 3 4 5 4 + 7710 q s + 68715 q s - 117465 q s + 59175 q s - 7077 s - 9460 n 3 3 2 2 2 2 2 - 9070 n q + 37840 n s + 29100 n q + 27210 n q s - 56760 n s 3 2 2 3 4 + 39650 n q - 58200 n q s - 27210 n q s + 37840 n s + 8780 q 3 2 2 3 4 3 2 - 39650 q s + 29100 q s + 9070 q s - 9460 s - 7055 n - 20985 n q 2 2 2 3 + 21165 n s - 14865 n q + 41970 n q s - 21165 n s + 1945 q 2 2 3 2 2 + 14865 q s - 20985 q s + 7055 s - 30 n - 2436 n q + 60 n s - 4566 q / 4 \ 2 |d | + 2436 q s - 30 s + 396 n + 1260 q - 396 s - 144) |--- A[n + 1](r, s)| | 4 | \ds / / 10 9 9 8 2 8 8 2 7 3 / ((n + 4 n q - 4 n s + 6 n q - 12 n q s + 6 n s + 4 n q / 7 2 7 2 7 3 6 4 6 3 6 2 2 - 12 n q s + 12 n q s - 4 n s + n q - 4 n q s + 6 n q s 6 3 6 4 9 8 8 7 2 7 - 4 n q s + n s + 4 n + 18 n q - 18 n s + 30 n q - 60 n q s 7 2 6 3 6 2 6 2 6 3 5 4 + 30 n s + 22 n q - 66 n q s + 66 n q s - 22 n s + 6 n q 5 3 5 2 2 5 3 5 4 8 7 - 24 n q s + 36 n q s - 24 n q s + 6 n s + 2 n + 22 n q 7 6 2 6 6 2 5 3 5 2 - 22 n s + 53 n q - 106 n q s + 53 n s + 48 n q - 144 n q s 5 2 5 3 4 4 4 3 4 2 2 + 144 n q s - 48 n s + 15 n q - 60 n q s + 90 n q s 4 3 4 4 7 6 6 5 2 5 - 60 n q s + 15 n s - 14 n - 20 n q + 20 n s + 24 n q - 48 n q s 5 2 4 3 4 2 4 2 4 3 3 4 + 24 n s + 50 n q - 150 n q s + 150 n q s - 50 n s + 20 n q 3 3 3 2 2 3 3 3 4 6 5 - 80 n q s + 120 n q s - 80 n q s + 20 n s - 28 n - 78 n q 5 4 2 4 4 2 3 3 3 2 + 78 n s - 45 n q + 90 n q s - 45 n s + 20 n q - 60 n q s 3 2 3 3 2 4 2 3 2 2 2 2 3 + 60 n q s - 20 n s + 15 n q - 60 n q s + 90 n q s - 60 n q s 2 4 5 4 4 3 2 3 3 2 + 15 n s - 14 n - 76 n q + 76 n s - 74 n q + 148 n q s - 74 n s 2 3 2 2 2 2 2 3 4 3 - 6 n q + 18 n q s - 18 n q s + 6 n s + 6 n q - 24 n q s 2 2 3 4 4 3 3 2 2 + 36 n q s - 24 n q s + 6 n s + 14 n - 22 n q + 22 n s - 45 n q 2 2 2 3 2 2 3 4 + 90 n q s - 45 n s - 8 n q + 24 n q s - 24 n q s + 8 n s + q 3 2 2 3 4 3 2 2 2 - 4 q s + 6 q s - 4 q s + s + 22 n + 12 n q - 12 n s - 12 n q 2 3 2 2 3 2 + 24 n q s - 12 n s - 2 q + 6 q s - 6 q s + 2 s + 11 n + 10 n q 2 2 2 - 10 n s - q + 2 q s - s + 2 n + 2 q - 2 s) (q + n - s + 1) %1) - ( 10 9 2 9 8 3 8 2 8 2 6 n q + 30 n q - 60 n q s + 60 n q - 270 n q s + 270 n q s 7 4 7 3 7 2 2 7 3 6 5 + 60 n q - 480 n q s + 1080 n q s - 720 n q s + 30 n q 6 4 6 3 2 6 2 3 6 4 5 6 - 420 n q s + 1680 n q s - 2520 n q s + 1260 n q s + 6 n q 5 5 5 4 2 5 3 3 5 2 4 - 180 n q s + 1260 n q s - 3360 n q s + 3780 n q s 5 5 4 6 4 5 2 4 4 3 4 3 4 - 1512 n q s - 30 n q s + 450 n q s - 2100 n q s + 4200 n q s 4 2 5 4 6 3 6 2 3 5 3 - 3780 n q s + 1260 n q s + 60 n q s - 600 n q s 3 4 4 3 3 5 3 2 6 3 7 + 2100 n q s - 3360 n q s + 2520 n q s - 720 n q s 2 6 3 2 5 4 2 4 5 2 3 6 - 60 n q s + 450 n q s - 1260 n q s + 1680 n q s 2 2 7 2 8 6 4 5 5 4 6 - 1080 n q s + 270 n q s + 30 n q s - 180 n q s + 420 n q s 3 7 2 8 9 6 5 5 6 4 7 - 480 n q s + 270 n q s - 60 n q s - 6 q s + 30 q s - 60 q s 3 8 2 9 10 10 9 9 8 2 + 60 q s - 30 q s + 6 q s - 15 n - 90 n q + 150 n s - 180 n q 8 8 2 7 3 7 2 7 2 + 810 n q s - 675 n s - 120 n q + 1440 n q s - 3240 n q s 7 3 6 4 6 3 6 2 2 6 3 + 1800 n s + 45 n q + 840 n q s - 5040 n q s + 7560 n q s 6 4 5 5 5 4 5 3 2 5 2 3 - 3150 n s + 90 n q - 270 n q s - 2520 n q s + 10080 n q s 5 4 5 5 4 6 4 5 4 4 2 - 11340 n q s + 3780 n s + 30 n q - 450 n q s + 675 n q s 4 3 3 4 2 4 4 5 4 6 + 4200 n q s - 12600 n q s + 11340 n q s - 3150 n s 3 6 3 5 2 3 4 3 3 3 4 - 120 n q s + 900 n q s - 900 n q s - 4200 n q s 3 2 5 3 6 3 7 2 6 2 2 5 3 + 10080 n q s - 7560 n q s + 1800 n s + 180 n q s - 900 n q s 2 4 4 2 3 5 2 2 6 2 7 2 8 + 675 n q s + 2520 n q s - 5040 n q s + 3240 n q s - 675 n s 6 3 5 4 4 5 3 6 2 7 - 120 n q s + 450 n q s - 270 n q s - 840 n q s + 1440 n q s 8 9 6 4 5 5 4 6 3 7 - 810 n q s + 150 n s + 30 q s - 90 q s + 45 q s + 120 q s 2 8 9 10 9 8 8 7 2 - 180 q s + 90 q s - 15 s + 20 n - 60 n q - 180 n s - 480 n q 7 7 2 6 3 6 2 6 2 + 480 n q s + 720 n s - 820 n q + 3360 n q s - 1680 n q s 6 3 5 4 5 3 5 2 2 5 3 - 1680 n s - 480 n q + 4920 n q s - 10080 n q s + 3360 n q s 5 4 4 4 4 3 2 4 2 3 + 2520 n s + 2400 n q s - 12300 n q s + 16800 n q s 4 4 4 5 3 6 3 4 2 3 3 3 - 4200 n q s - 2520 n s + 60 n q - 4800 n q s + 16400 n q s 3 2 4 3 5 3 6 2 6 2 4 3 - 16800 n q s + 3360 n q s + 1680 n s - 180 n q s + 4800 n q s 2 3 4 2 2 5 2 6 2 7 6 2 - 12300 n q s + 10080 n q s - 1680 n q s - 720 n s + 180 n q s 4 4 3 5 2 6 7 8 - 2400 n q s + 4920 n q s - 3360 n q s + 480 n q s + 180 n s 6 3 4 5 3 6 2 7 8 9 8 - 60 q s + 480 q s - 820 q s + 480 q s - 60 q s - 20 s + 180 n 7 7 6 2 6 6 2 5 3 + 780 n q - 1440 n s + 825 n q - 5460 n q s + 5040 n s - 390 n q 5 2 5 2 5 3 4 4 4 3 - 4950 n q s + 16380 n q s - 10080 n s - 975 n q + 1950 n q s 4 2 2 4 3 4 4 3 5 3 4 + 12375 n q s - 27300 n q s + 12600 n s - 300 n q + 3900 n q s 3 3 2 3 2 3 3 4 3 5 2 6 - 3900 n q s - 16500 n q s + 27300 n q s - 10080 n s + 60 n q 2 5 2 4 2 2 3 3 2 2 4 + 900 n q s - 5850 n q s + 3900 n q s + 12375 n q s 2 5 2 6 6 5 2 4 3 - 16380 n q s + 5040 n s - 120 n q s - 900 n q s + 3900 n q s 3 4 2 5 6 7 6 2 - 1950 n q s - 4950 n q s + 5460 n q s - 1440 n s + 60 q s 5 3 4 4 3 5 2 6 7 8 + 300 q s - 975 q s + 390 q s + 825 q s - 780 q s + 180 s 7 6 6 5 2 5 5 2 + 16 n + 1060 n q - 112 n s + 2814 n q - 6360 n q s + 336 n s 4 3 4 2 4 2 4 3 3 4 + 1950 n q - 14070 n q s + 15900 n q s - 560 n s - 300 n q 3 3 3 2 2 3 3 3 4 2 5 - 7800 n q s + 28140 n q s - 21200 n q s + 560 n s - 450 n q 2 4 2 3 2 2 2 3 2 4 + 900 n q s + 11700 n q s - 28140 n q s + 15900 n q s 2 5 6 5 4 2 3 3 - 336 n s + 30 n q + 900 n q s - 900 n q s - 7800 n q s 2 4 5 6 6 5 2 4 3 + 14070 n q s - 6360 n q s + 112 n s - 30 q s - 450 q s + 300 q s 3 4 2 5 6 7 6 5 + 1950 q s - 2814 q s + 1060 q s - 16 s - 698 n - 1248 n q 5 4 2 4 4 2 3 3 + 4188 n s + 1275 n q + 6240 n q s - 10470 n s + 2860 n q 3 2 3 2 3 3 2 4 2 3 - 5100 n q s - 12480 n q s + 13960 n s + 735 n q - 8580 n q s 2 2 2 2 3 2 4 5 4 + 7650 n q s + 12480 n q s - 10470 n s - 270 n q - 1470 n q s 3 2 2 3 4 5 6 5 + 8580 n q s - 5100 n q s - 6240 n q s + 4188 n s + 6 q + 270 q s 4 2 3 3 2 4 5 6 5 + 735 q s - 2860 q s + 1275 q s + 1248 q s - 698 s - 744 n 4 4 3 2 3 3 2 - 3240 n q + 3720 n s - 2340 n q + 12960 n q s - 7440 n s 2 3 2 2 2 2 2 3 4 + 1080 n q + 7020 n q s - 19440 n q s + 7440 n s + 720 n q 3 2 2 3 4 5 4 - 2160 n q s - 7020 n q s + 12960 n q s - 3720 n s - 60 q - 720 q s 3 2 2 3 4 5 4 3 + 1080 q s + 2340 q s - 3240 q s + 744 s + 380 n - 1660 n q 3 2 2 2 2 2 3 - 1520 n s - 2865 n q + 4980 n q s + 2280 n s - 270 n q 2 2 3 4 3 2 2 + 5730 n q s - 4980 n q s - 1520 n s + 195 q + 270 q s - 2865 q s 3 4 3 2 2 2 + 1660 q s + 380 s + 1040 n + 630 n q - 3120 n s - 1080 n q 2 3 2 2 3 - 1260 n q s + 3120 n s - 190 q + 1080 q s + 630 q s - 1040 s 2 2 2 + 561 n + 810 n q - 1122 n s - 111 q - 810 q s + 561 s + 52 n + 196 q / 5 \ |d | / 11 10 10 9 2 - 52 s - 24) |--- A[n + 1](r, s)| / ((n + 5 n q - 5 n s + 10 n q | 5 | / \ds / 9 9 2 8 3 8 2 8 2 8 3 - 20 n q s + 10 n s + 10 n q - 30 n q s + 30 n q s - 10 n s 7 4 7 3 7 2 2 7 3 7 4 6 5 + 5 n q - 20 n q s + 30 n q s - 20 n q s + 5 n s + n q 6 4 6 3 2 6 2 3 6 4 6 5 10 - 5 n q s + 10 n q s - 10 n q s + 5 n q s - n s + n 9 9 8 2 8 8 2 7 3 + 10 n q - 10 n s + 30 n q - 60 n q s + 30 n s + 40 n q 7 2 7 2 7 3 6 4 6 3 - 120 n q s + 120 n q s - 40 n s + 25 n q - 100 n q s 6 2 2 6 3 6 4 5 5 5 4 + 150 n q s - 100 n q s + 25 n s + 6 n q - 30 n q s 5 3 2 5 2 3 5 4 5 5 9 8 + 60 n q s - 60 n q s + 30 n q s - 6 n s - 10 n - 30 n q 8 7 2 7 7 2 6 3 6 2 + 30 n s - 15 n q + 30 n q s - 15 n s + 35 n q - 105 n q s 6 2 6 3 5 4 5 3 5 2 2 + 105 n q s - 35 n s + 45 n q - 180 n q s + 270 n q s 5 3 5 4 4 5 4 4 4 3 2 - 180 n q s + 45 n s + 15 n q - 75 n q s + 150 n q s 4 2 3 4 4 4 5 8 7 7 - 150 n q s + 75 n q s - 15 n s - 20 n - 100 n q + 100 n s 6 2 6 6 2 5 3 5 2 - 155 n q + 310 n q s - 155 n s - 70 n q + 210 n q s 5 2 5 3 4 4 4 3 4 2 2 - 210 n q s + 70 n s + 25 n q - 100 n q s + 150 n q s 4 3 4 4 3 5 3 4 3 3 2 - 100 n q s + 25 n s + 20 n q - 100 n q s + 200 n q s 3 2 3 3 4 3 5 7 6 6 - 200 n q s + 100 n q s - 20 n s + 14 n - 46 n q + 46 n s 5 2 5 5 2 4 3 4 2 - 195 n q + 390 n q s - 195 n s - 175 n q + 525 n q s 4 2 4 3 3 4 3 3 3 2 2 - 525 n q s + 175 n s - 25 n q + 100 n q s - 150 n q s 3 3 3 4 2 5 2 4 2 3 2 + 100 n q s - 25 n s + 15 n q - 75 n q s + 150 n q s 2 2 3 2 4 2 5 6 5 5 - 150 n q s + 75 n q s - 15 n s + 70 n + 144 n q - 144 n s 4 2 4 4 2 3 3 3 2 3 2 - 15 n q + 30 n q s - 15 n s - 140 n q + 420 n q s - 420 n q s 3 3 2 4 2 3 2 2 2 2 3 + 140 n s - 45 n q + 180 n q s - 270 n q s + 180 n q s 2 4 5 4 3 2 2 3 4 - 45 n s + 6 n q - 30 n q s + 60 n q s - 60 n q s + 30 n q s 5 5 4 4 3 2 3 - 6 n s + 56 n + 220 n q - 220 n s + 155 n q - 310 n q s 3 2 2 3 2 2 2 2 2 3 4 + 155 n s - 35 n q + 105 n q s - 105 n q s + 35 n s - 25 n q 3 2 2 3 4 5 4 3 2 + 100 n q s - 150 n q s + 100 n q s - 25 n s + q - 5 q s + 10 q s 2 3 4 5 4 3 3 2 2 - 10 q s + 5 q s - s - 20 n + 100 n q - 100 n s + 135 n q 2 2 2 3 2 2 3 - 270 n q s + 135 n s + 10 n q - 30 n q s + 30 n q s - 10 n s 4 3 2 2 3 4 3 2 2 - 5 q + 20 q s - 30 q s + 20 q s - 5 s - 55 n - 15 n q + 15 n s 2 2 3 2 2 3 2 + 45 n q - 90 n q s + 45 n s + 5 q - 15 q s + 15 q s - 5 s - 31 n 2 2 - 26 n q + 26 n s + 5 q - 10 q s + 5 s - 6 n - 6 q + 6 s) 6 5 4 2 3 3 2 4 5 (q + n - s + 1)) - (n - 6 n s + 15 n s - 20 n s + 15 n s - 6 n s 6 5 4 3 2 2 3 4 5 4 + s + 6 n - 30 n s + 60 n s - 60 n s + 30 n s - 6 s + 15 n 3 2 2 3 4 3 2 2 3 - 60 n s + 90 n s - 60 n s + 15 s + 20 n - 60 n s + 60 n s - 20 s / 6 \ 2 2 |d | / 7 + 15 n - 30 n s + 15 s + 6 n - 6 s + 1) |--- A[n + 1](r, s)| / (n | 6 | / \ds / 6 6 6 5 5 5 4 4 4 + n q - n s + 7 n + 6 n q - 6 n s + 21 n + 15 n q - 15 n s + 35 n 3 3 3 2 2 2 + 20 n q - 20 n s + 35 n + 15 n q - 15 n s + 21 n + 6 n q - 6 n s + 7 n + q - s + 1) = 0 4 3 3 2 2 2 2 2 3 2 %1 := n + 4 n q - 4 n s + 6 n q - 12 n q s + 6 n s + 4 n q - 12 n q s 2 3 4 3 2 2 3 4 3 + 12 n q s - 4 n s + q - 4 q s + 6 q s - 4 q s + s - 6 n 2 2 2 2 3 2 - 18 n q + 18 n s - 18 n q + 36 n q s - 18 n s - 6 q + 18 q s 2 3 2 2 2 - 18 q s + 6 s + 11 n + 22 n q - 22 n s + 11 q - 22 q s + 11 s - 6 n - 6 q + 6 s 2 2 2 %2 := n + 2 n q - 2 n s + q - 2 q s + s - n - q + s and in Maple notation (p^6-5*p^5*r+p^5*s+10*p^4*r^2-5*p^4*r*s-10*p^3*r^3+10*p^3*r^2*s+5*p^2*r^4-10*p^ 2*r^3*s-p*r^5+5*p*r^4*s-r^5*s-21*p^5+85*p^4*r-20*p^4*s-130*p^3*r^2+80*p^3*r*s+ 90*p^2*r^3-120*p^2*r^2*s-25*p*r^4+80*p*r^3*s+r^5-20*r^4*s+175*p^4-545*p^3*r+155 *p^3*s+585*p^2*r^2-465*p^2*r*s-235*p*r^3+465*p*r^2*s+20*r^4-155*r^3*s-735*p^3+ 1625*p^2*r-580*p^2*s-1045*p*r^2+1160*p*r*s+155*r^3-580*r^2*s+1624*p^2-2204*p*r+ 1044*p*s+580*r^2-1044*r*s-1764*p+1044*r-720*s+720)/(p*r+p*s-r^2-r*s-r-s)/(p-r-1 )^4*A[n](r,s)-(5*p^10-44*p^9*r+6*p^9*s+171*p^8*r^2-54*p^8*r*s-384*p^7*r^3+216*p ^7*r^2*s+546*p^6*r^4-504*p^6*r^3*s-504*p^5*r^5+756*p^5*r^4*s+294*p^4*r^6-756*p^ 4*r^5*s-96*p^3*r^7+504*p^3*r^6*s+9*p^2*r^8-216*p^2*r^7*s+4*p*r^9+54*p*r^8*s-r^ 10-6*r^9*s-135*p^9+1062*p^8*r-153*p^8*s-3636*p^7*r^2+1224*p^7*r*s+7056*p^6*r^3-\ 4284*p^6*r^2*s-8442*p^5*r^4+8568*p^5*r^3*s+6300*p^4*r^5-10710*p^4*r^4*s-2772*p^ 3*r^6+8568*p^3*r^5*s+576*p^2*r^7-4284*p^2*r^6*s+9*p*r^8+1224*p*r^7*s-18*r^9-153 *r^8*s+1575*p^8-10936*p^7*r+1664*p^7*s+32452*p^6*r^2-11648*p^6*r*s-53256*p^5*r^ 3+34944*p^5*r^2*s+52010*p^4*r^4-58240*p^4*r^3*s-29960*p^3*r^5+58240*p^3*r^4*s+ 9156*p^2*r^6-34944*p^2*r^5*s-952*p*r^7+11648*p*r^6*s-89*r^8-1664*r^7*s-10470*p^ 7+63138*p^6*r-10152*p^6*s-158958*p^5*r^2+60912*p^5*r*s+214170*p^4*r^3-152280*p^ 4*r^2*s-163410*p^3*r^4+203040*p^3*r^3*s+67590*p^2*r^5-152280*p^2*r^4*s-12378*p* r^6+60912*p*r^5*s+318*r^7-10152*r^6*s+44026*p^6-225710*p^5*r+38446*p^5*s+468160 *p^4*r^2-192230*p^4*r*s-496060*p^3*r^3+384460*p^3*r^2*s+275930*p^2*r^4-384460*p ^2*r^3*s-71926*p*r^5+192230*p*r^4*s+5580*r^6-38446*r^5*s-122766*p^5+519564*p^4* r-94266*p^4*s-850596*p^3*r^2+377064*p^3*r*s+662064*p^2*r^3-565596*p^2*r^2*s-\ 236766*p*r^4+377064*p*r^3*s+28500*r^5-94266*r^4*s+230750*p^4-772382*p^3*r+ 150618*p^3*s+932646*p^2*r^2-451854*p^2*r*s-471146*p*r^3+451854*p*r^2*s+80132*r^ 4-150618*r^3*s-289665*p^3+716886*p^2*r-152109*p^2*s-564777*p*r^2+304218*p*r*s+ 137556*r^3-152109*r^2*s+233044*p^2-377582*p*r+88506*p*s+144538*r^2-88506*r*s-\ 108684*p+86004*r-22680*s+22320)/(p-r-1)/(p^2*r+p^2*s-2*p*r^2-2*p*r*s+r^3+r^2*s-\ 3*p*r-3*p*s+3*r^2+3*r*s+2*r+2*s)/(p^2-2*p*r+r^2-3*p+3*r+2)^3*diff(A[n](r,s),r)+ (10*p^12-105*p^11*r+15*p^11*s+495*p^10*r^2-165*p^10*r*s-1375*p^9*r^3+825*p^9*r^ 2*s+2475*p^8*r^4-2475*p^8*r^3*s-2970*p^7*r^5+4950*p^7*r^4*s+2310*p^6*r^6-6930*p 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217320*n*r^4-120*p^5+5220*p^4*r-53280*p^3*r^2+183060*p^2*r^3-230760*p*r^4+89616 *r^5-4860*n^4-40880*n^3*p+21440*n^3*r+64365*n^2*p^2-251370*n^2*p*r+157845*n^2*r ^2-17850*n*p^3+182280*n*p^2*r-433650*n*p*r^2+249780*n*r^3+945*p^4-21630*p^3*r+ 123585*p^2*r^2-226940*p*r^3+119180*r^4+7920*n^3-57120*n^2*p+80880*n^2*r+35490*n *p^2-185220*n*p*r+173490*n*r^2-3710*p^3+46620*p^2*r-139230*p*r^2+104240*r^3+ 16740*n^2-33432*n*p+66912*n*r+7539*p^2-48510*p*r+57711*r^2+11016*n-7336*p+18352 *r+2556)/(n^6*p^5-5*n^6*p^4*r+10*n^6*p^3*r^2-10*n^6*p^2*r^3+5*n^6*p*r^4-n^6*r^5 -15*n^6*p^4+60*n^6*p^3*r-90*n^6*p^2*r^2+60*n^6*p*r^3-15*n^6*r^4+6*n^5*p^5-30*n^ 5*p^4*r+60*n^5*p^3*r^2-60*n^5*p^2*r^3+30*n^5*p*r^4-6*n^5*r^5+85*n^6*p^3-255*n^6 *p^2*r+255*n^6*p*r^2-85*n^6*r^3-90*n^5*p^4+360*n^5*p^3*r-540*n^5*p^2*r^2+360*n^ 5*p*r^3-90*n^5*r^4+15*n^4*p^5-75*n^4*p^4*r+150*n^4*p^3*r^2-150*n^4*p^2*r^3+75*n ^4*p*r^4-15*n^4*r^5-225*n^6*p^2+450*n^6*p*r-225*n^6*r^2+510*n^5*p^3-1530*n^5*p^ 2*r+1530*n^5*p*r^2-510*n^5*r^3-225*n^4*p^4+900*n^4*p^3*r-1350*n^4*p^2*r^2+900*n ^4*p*r^3-225*n^4*r^4+20*n^3*p^5-100*n^3*p^4*r+200*n^3*p^3*r^2-200*n^3*p^2*r^3+ 100*n^3*p*r^4-20*n^3*r^5+274*n^6*p-274*n^6*r-1350*n^5*p^2+2700*n^5*p*r-1350*n^5 *r^2+1275*n^4*p^3-3825*n^4*p^2*r+3825*n^4*p*r^2-1275*n^4*r^3-300*n^3*p^4+1200*n ^3*p^3*r-1800*n^3*p^2*r^2+1200*n^3*p*r^3-300*n^3*r^4+15*n^2*p^5-75*n^2*p^4*r+ 150*n^2*p^3*r^2-150*n^2*p^2*r^3+75*n^2*p*r^4-15*n^2*r^5-120*n^6+1644*n^5*p-1644 *n^5*r-3375*n^4*p^2+6750*n^4*p*r-3375*n^4*r^2+1700*n^3*p^3-5100*n^3*p^2*r+5100* n^3*p*r^2-1700*n^3*r^3-225*n^2*p^4+900*n^2*p^3*r-1350*n^2*p^2*r^2+900*n^2*p*r^3 -225*n^2*r^4+6*n*p^5-30*n*p^4*r+60*n*p^3*r^2-60*n*p^2*r^3+30*n*p*r^4-6*n*r^5-\ 720*n^5+4110*n^4*p-4110*n^4*r-4500*n^3*p^2+9000*n^3*p*r-4500*n^3*r^2+1275*n^2*p ^3-3825*n^2*p^2*r+3825*n^2*p*r^2-1275*n^2*r^3-90*n*p^4+360*n*p^3*r-540*n*p^2*r^ 2+360*n*p*r^3-90*n*r^4+p^5-5*p^4*r+10*p^3*r^2-10*p^2*r^3+5*p*r^4-r^5-1800*n^4+ 5480*n^3*p-5480*n^3*r-3375*n^2*p^2+6750*n^2*p*r-3375*n^2*r^2+510*n*p^3-1530*n*p ^2*r+1530*n*p*r^2-510*n*r^3-15*p^4+60*p^3*r-90*p^2*r^2+60*p*r^3-15*r^4-2400*n^3 +4110*n^2*p-4110*n^2*r-1350*n*p^2+2700*n*p*r-1350*n*r^2+85*p^3-255*p^2*r+255*p* r^2-85*r^3-1800*n^2+1644*n*p-1644*n*r-225*p^2+450*p*r-225*r^2-720*n+274*p-274*r -120)/(r+s)*diff(diff(diff(diff(diff(A[n+1](r,s),r),r),r),r),r)-(n^6+6*n^5*r+15 *n^4*r^2+20*n^3*r^3+15*n^2*r^4+6*n*r^5+r^6+6*n^5+30*n^4*r+60*n^3*r^2+60*n^2*r^3 +30*n*r^4+6*r^5+15*n^4+60*n^3*r+90*n^2*r^2+60*n*r^3+15*r^4+20*n^3+60*n^2*r+60*n *r^2+20*r^3+15*n^2+30*n*r+15*r^2+6*n+6*r+1)/(n^6+6*n^5+15*n^4+20*n^3+15*n^2+6*n +1)/(r+s)*diff(diff(diff(diff(diff(diff(A[n+1](r,s),r),r),r),r),r),r) = 0 -(n^4+4*n^3*q-4*n^3*s+6*n^2*q^2-12*n^2*q*s+6*n^2*s^2+4*n*q^3-12*n*q^2*s+12*n*q* s^2-4*n*s^3+q^4-4*q^3*s+6*q^2*s^2-4*q*s^3+s^4-10*n^3-30*n^2*q+30*n^2*s-30*n*q^2 +60*n*q*s-30*n*s^2-10*q^3+30*q^2*s-30*q*s^2+10*s^3+35*n^2+70*n*q-70*n*s+35*q^2-\ 70*q*s+35*s^2-50*n-50*q+50*s+24)/(n+q-s)^4*A[n](r,s)+(5*n^7+35*n^6*q-35*n^6*s+ 105*n^5*q^2-210*n^5*q*s+105*n^5*s^2+175*n^4*q^3-525*n^4*q^2*s+525*n^4*q*s^2-175 *n^4*s^3+175*n^3*q^4-700*n^3*q^3*s+1050*n^3*q^2*s^2-700*n^3*q*s^3+175*n^3*s^4+ 105*n^2*q^5-525*n^2*q^4*s+1050*n^2*q^3*s^2-1050*n^2*q^2*s^3+525*n^2*q*s^4-105*n ^2*s^5+35*n*q^6-210*n*q^5*s+525*n*q^4*s^2-700*n*q^3*s^3+525*n*q^2*s^4-210*n*q*s ^5+35*n*s^6+5*q^7-35*q^6*s+105*q^5*s^2-175*q^4*s^3+175*q^3*s^4-105*q^2*s^5+35*q *s^6-5*s^7-55*n^6-330*n^5*q+330*n^5*s-825*n^4*q^2+1650*n^4*q*s-825*n^4*s^2-1100 *n^3*q^3+3300*n^3*q^2*s-3300*n^3*q*s^2+1100*n^3*s^3-825*n^2*q^4+3300*n^2*q^3*s-\ 4950*n^2*q^2*s^2+3300*n^2*q*s^3-825*n^2*s^4-330*n*q^5+1650*n*q^4*s-3300*n*q^3*s ^2+3300*n*q^2*s^3-1650*n*q*s^4+330*n*s^5-55*q^6+330*q^5*s-825*q^4*s^2+1100*q^3* s^3-825*q^2*s^4+330*q*s^5-55*s^6+230*n^5+1150*n^4*q-1150*n^4*s+2300*n^3*q^2-\ 4600*n^3*q*s+2300*n^3*s^2+2300*n^2*q^3-6900*n^2*q^2*s+6900*n^2*q*s^2-2300*n^2*s ^3+1150*n*q^4-4600*n*q^3*s+6900*n*q^2*s^2-4600*n*q*s^3+1150*n*s^4+230*q^5-1150* q^4*s+2300*q^3*s^2-2300*q^2*s^3+1150*q*s^4-230*s^5-475*n^4-1900*n^3*q+1900*n^3* s-2850*n^2*q^2+5700*n^2*q*s-2850*n^2*s^2-1900*n*q^3+5700*n*q^2*s-5700*n*q*s^2+ 1900*n*s^3-475*q^4+1900*q^3*s-2850*q^2*s^2+1900*q*s^3-475*s^4+546*n^3+1638*n^2* q-1638*n^2*s+1638*n*q^2-3276*n*q*s+1638*n*s^2+546*q^3-1638*q^2*s+1638*q*s^2-546 *s^3-379*n^2-758*n*q+758*n*s-379*q^2+758*q*s-379*s^2+146*n+146*q-146*s-24)/(n+q -s)/(n^2+2*n*q-2*n*s+q^2-2*q*s+s^2-n-q+s)^3*diff(A[n](r,s),s)-(10*n^8+80*n^7*q-\ 80*n^7*s+280*n^6*q^2-560*n^6*q*s+280*n^6*s^2+560*n^5*q^3-1680*n^5*q^2*s+1680*n^ 5*q*s^2-560*n^5*s^3+700*n^4*q^4-2800*n^4*q^3*s+4200*n^4*q^2*s^2-2800*n^4*q*s^3+ 700*n^4*s^4+560*n^3*q^5-2800*n^3*q^4*s+5600*n^3*q^3*s^2-5600*n^3*q^2*s^3+2800*n ^3*q*s^4-560*n^3*s^5+280*n^2*q^6-1680*n^2*q^5*s+4200*n^2*q^4*s^2-5600*n^2*q^3*s ^3+4200*n^2*q^2*s^4-1680*n^2*q*s^5+280*n^2*s^6+80*n*q^7-560*n*q^6*s+1680*n*q^5* s^2-2800*n*q^4*s^3+2800*n*q^3*s^4-1680*n*q^2*s^5+560*n*q*s^6-80*n*s^7+10*q^8-80 *q^7*s+280*q^6*s^2-560*q^5*s^3+700*q^4*s^4-560*q^3*s^5+280*q^2*s^6-80*q*s^7+10* s^8-130*n^7-910*n^6*q+910*n^6*s-2730*n^5*q^2+5460*n^5*q*s-2730*n^5*s^2-4550*n^4 *q^3+13650*n^4*q^2*s-13650*n^4*q*s^2+4550*n^4*s^3-4550*n^3*q^4+18200*n^3*q^3*s-\ 27300*n^3*q^2*s^2+18200*n^3*q*s^3-4550*n^3*s^4-2730*n^2*q^5+13650*n^2*q^4*s-\ 27300*n^2*q^3*s^2+27300*n^2*q^2*s^3-13650*n^2*q*s^4+2730*n^2*s^5-910*n*q^6+5460 *n*q^5*s-13650*n*q^4*s^2+18200*n*q^3*s^3-13650*n*q^2*s^4+5460*n*q*s^5-910*n*s^6 -130*q^7+910*q^6*s-2730*q^5*s^2+4550*q^4*s^3-4550*q^3*s^4+2730*q^2*s^5-910*q*s^ 6+130*s^7+685*n^6+4110*n^5*q-4110*n^5*s+10275*n^4*q^2-20550*n^4*q*s+10275*n^4*s ^2+13700*n^3*q^3-41100*n^3*q^2*s+41100*n^3*q*s^2-13700*n^3*s^3+10275*n^2*q^4-\ 41100*n^2*q^3*s+61650*n^2*q^2*s^2-41100*n^2*q*s^3+10275*n^2*s^4+4110*n*q^5-\ 20550*n*q^4*s+41100*n*q^3*s^2-41100*n*q^2*s^3+20550*n*q*s^4-4110*n*s^5+685*q^6-\ 4110*q^5*s+10275*q^4*s^2-13700*q^3*s^3+10275*q^2*s^4-4110*q*s^5+685*s^6-1915*n^ 5-9575*n^4*q+9575*n^4*s-19150*n^3*q^2+38300*n^3*q*s-19150*n^3*s^2-19150*n^2*q^3 +57450*n^2*q^2*s-57450*n^2*q*s^2+19150*n^2*s^3-9575*n*q^4+38300*n*q^3*s-57450*n *q^2*s^2+38300*n*q*s^3-9575*n*s^4-1915*q^5+9575*q^4*s-19150*q^3*s^2+19150*q^2*s ^3-9575*q*s^4+1915*s^5+3124*n^4+12496*n^3*q-12496*n^3*s+18744*n^2*q^2-37488*n^2 *q*s+18744*n^2*s^2+12496*n*q^3-37488*n*q^2*s+37488*n*q*s^2-12496*n*s^3+3124*q^4 -12496*q^3*s+18744*q^2*s^2-12496*q*s^3+3124*s^4-3076*n^3-9228*n^2*q+9228*n^2*s-\ 9228*n*q^2+18456*n*q*s-9228*n*s^2-3076*q^3+9228*q^2*s-9228*q*s^2+3076*s^3+1832* n^2+3664*n*q-3664*n*s+1832*q^2-3664*q*s+1832*s^2-632*n-632*q+632*s+96)/(n^2+2*n *q-2*n*s+q^2-2*q*s+s^2-n-q+s)/(n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+3*n*s^2+q^3-\ 3*q^2*s+3*q*s^2-s^3-3*n^2-6*n*q+6*n*s-3*q^2+6*q*s-3*s^2+2*n+2*q-2*s)^2*diff( diff(A[n](r,s),s),s)+(10*n^7+70*n^6*q-70*n^6*s+210*n^5*q^2-420*n^5*q*s+210*n^5* s^2+350*n^4*q^3-1050*n^4*q^2*s+1050*n^4*q*s^2-350*n^4*s^3+350*n^3*q^4-1400*n^3* q^3*s+2100*n^3*q^2*s^2-1400*n^3*q*s^3+350*n^3*s^4+210*n^2*q^5-1050*n^2*q^4*s+ 2100*n^2*q^3*s^2-2100*n^2*q^2*s^3+1050*n^2*q*s^4-210*n^2*s^5+70*n*q^6-420*n*q^5 *s+1050*n*q^4*s^2-1400*n*q^3*s^3+1050*n*q^2*s^4-420*n*q*s^5+70*n*s^6+10*q^7-70* q^6*s+210*q^5*s^2-350*q^4*s^3+350*q^3*s^4-210*q^2*s^5+70*q*s^6-10*s^7-130*n^6-\ 780*n^5*q+780*n^5*s-1950*n^4*q^2+3900*n^4*q*s-1950*n^4*s^2-2600*n^3*q^3+7800*n^ 3*q^2*s-7800*n^3*q*s^2+2600*n^3*s^3-1950*n^2*q^4+7800*n^2*q^3*s-11700*n^2*q^2*s ^2+7800*n^2*q*s^3-1950*n^2*s^4-780*n*q^5+3900*n*q^4*s-7800*n*q^3*s^2+7800*n*q^2 *s^3-3900*n*q*s^4+780*n*s^5-130*q^6+780*q^5*s-1950*q^4*s^2+2600*q^3*s^3-1950*q^ 2*s^4+780*q*s^5-130*s^6+675*n^5+3375*n^4*q-3375*n^4*s+6750*n^3*q^2-13500*n^3*q* s+6750*n^3*s^2+6750*n^2*q^3-20250*n^2*q^2*s+20250*n^2*q*s^2-6750*n^2*s^3+3375*n *q^4-13500*n*q^3*s+20250*n*q^2*s^2-13500*n*q*s^3+3375*n*s^4+675*q^5-3375*q^4*s+ 6750*q^3*s^2-6750*q^2*s^3+3375*q*s^4-675*s^5-1800*n^4-7200*n^3*q+7200*n^3*s-\ 10800*n^2*q^2+21600*n^2*q*s-10800*n^2*s^2-7200*n*q^3+21600*n*q^2*s-21600*n*q*s^ 2+7200*n*s^3-1800*q^4+7200*q^3*s-10800*q^2*s^2+7200*q*s^3-1800*s^4+2631*n^3+ 7893*n^2*q-7893*n^2*s+7893*n*q^2-15786*n*q*s+7893*n*s^2+2631*q^3-7893*q^2*s+ 7893*q*s^2-2631*s^3-2082*n^2-4164*n*q+4164*n*s-2082*q^2+4164*q*s-2082*s^2+828*n +828*q-828*s-144)/(n^4+4*n^3*q-4*n^3*s+6*n^2*q^2-12*n^2*q*s+6*n^2*s^2+4*n*q^3-\ 12*n*q^2*s+12*n*q*s^2-4*n*s^3+q^4-4*q^3*s+6*q^2*s^2-4*q*s^3+s^4-6*n^3-18*n^2*q+ 18*n^2*s-18*n*q^2+36*n*q*s-18*n*s^2-6*q^3+18*q^2*s-18*q*s^2+6*s^3+11*n^2+22*n*q -22*n*s+11*q^2-22*q*s+11*s^2-6*n-6*q+6*s)/(n^3+3*n^2*q-3*n^2*s+3*n*q^2-6*n*q*s+ 3*n*s^2+q^3-3*q^2*s+3*q*s^2-s^3-3*n^2-6*n*q+6*n*s-3*q^2+6*q*s-3*s^2+2*n+2*q-2*s )*diff(diff(diff(A[n](r,s),s),s),s)-(5*n^4+20*n^3*q-20*n^3*s+30*n^2*q^2-60*n^2* q*s+30*n^2*s^2+20*n*q^3-60*n*q^2*s+60*n*q*s^2-20*n*s^3+5*q^4-20*q^3*s+30*q^2*s^ 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^4+270*q^3*s-2865*q^2*s^2+1660*q*s^3+380*s^4+1040*n^3+630*n^2*q-3120*n^2*s-1080 *n*q^2-1260*n*q*s+3120*n*s^2-190*q^3+1080*q^2*s+630*q*s^2-1040*s^3+561*n^2+810* n*q-1122*n*s-111*q^2-810*q*s+561*s^2+52*n+196*q-52*s-24)/(n^11+5*n^10*q-5*n^10* s+10*n^9*q^2-20*n^9*q*s+10*n^9*s^2+10*n^8*q^3-30*n^8*q^2*s+30*n^8*q*s^2-10*n^8* s^3+5*n^7*q^4-20*n^7*q^3*s+30*n^7*q^2*s^2-20*n^7*q*s^3+5*n^7*s^4+n^6*q^5-5*n^6* q^4*s+10*n^6*q^3*s^2-10*n^6*q^2*s^3+5*n^6*q*s^4-n^6*s^5+n^10+10*n^9*q-10*n^9*s+ 30*n^8*q^2-60*n^8*q*s+30*n^8*s^2+40*n^7*q^3-120*n^7*q^2*s+120*n^7*q*s^2-40*n^7* s^3+25*n^6*q^4-100*n^6*q^3*s+150*n^6*q^2*s^2-100*n^6*q*s^3+25*n^6*s^4+6*n^5*q^5 -30*n^5*q^4*s+60*n^5*q^3*s^2-60*n^5*q^2*s^3+30*n^5*q*s^4-6*n^5*s^5-10*n^9-30*n^ 8*q+30*n^8*s-15*n^7*q^2+30*n^7*q*s-15*n^7*s^2+35*n^6*q^3-105*n^6*q^2*s+105*n^6* q*s^2-35*n^6*s^3+45*n^5*q^4-180*n^5*q^3*s+270*n^5*q^2*s^2-180*n^5*q*s^3+45*n^5* s^4+15*n^4*q^5-75*n^4*q^4*s+150*n^4*q^3*s^2-150*n^4*q^2*s^3+75*n^4*q*s^4-15*n^4 *s^5-20*n^8-100*n^7*q+100*n^7*s-155*n^6*q^2+310*n^6*q*s-155*n^6*s^2-70*n^5*q^3+ 210*n^5*q^2*s-210*n^5*q*s^2+70*n^5*s^3+25*n^4*q^4-100*n^4*q^3*s+150*n^4*q^2*s^2 -100*n^4*q*s^3+25*n^4*s^4+20*n^3*q^5-100*n^3*q^4*s+200*n^3*q^3*s^2-200*n^3*q^2* s^3+100*n^3*q*s^4-20*n^3*s^5+14*n^7-46*n^6*q+46*n^6*s-195*n^5*q^2+390*n^5*q*s-\ 195*n^5*s^2-175*n^4*q^3+525*n^4*q^2*s-525*n^4*q*s^2+175*n^4*s^3-25*n^3*q^4+100* n^3*q^3*s-150*n^3*q^2*s^2+100*n^3*q*s^3-25*n^3*s^4+15*n^2*q^5-75*n^2*q^4*s+150* n^2*q^3*s^2-150*n^2*q^2*s^3+75*n^2*q*s^4-15*n^2*s^5+70*n^6+144*n^5*q-144*n^5*s-\ 15*n^4*q^2+30*n^4*q*s-15*n^4*s^2-140*n^3*q^3+420*n^3*q^2*s-420*n^3*q*s^2+140*n^ 3*s^3-45*n^2*q^4+180*n^2*q^3*s-270*n^2*q^2*s^2+180*n^2*q*s^3-45*n^2*s^4+6*n*q^5 -30*n*q^4*s+60*n*q^3*s^2-60*n*q^2*s^3+30*n*q*s^4-6*n*s^5+56*n^5+220*n^4*q-220*n ^4*s+155*n^3*q^2-310*n^3*q*s+155*n^3*s^2-35*n^2*q^3+105*n^2*q^2*s-105*n^2*q*s^2 +35*n^2*s^3-25*n*q^4+100*n*q^3*s-150*n*q^2*s^2+100*n*q*s^3-25*n*s^4+q^5-5*q^4*s +10*q^3*s^2-10*q^2*s^3+5*q*s^4-s^5-20*n^4+100*n^3*q-100*n^3*s+135*n^2*q^2-270*n ^2*q*s+135*n^2*s^2+10*n*q^3-30*n*q^2*s+30*n*q*s^2-10*n*s^3-5*q^4+20*q^3*s-30*q^ 2*s^2+20*q*s^3-5*s^4-55*n^3-15*n^2*q+15*n^2*s+45*n*q^2-90*n*q*s+45*n*s^2+5*q^3-\ 15*q^2*s+15*q*s^2-5*s^3-31*n^2-26*n*q+26*n*s+5*q^2-10*q*s+5*s^2-6*n-6*q+6*s)/(q +n-s+1)*diff(diff(diff(diff(diff(A[n+1](r,s),s),s),s),s),s)-(n^6-6*n^5*s+15*n^4 *s^2-20*n^3*s^3+15*n^2*s^4-6*n*s^5+s^6+6*n^5-30*n^4*s+60*n^3*s^2-60*n^2*s^3+30* n*s^4-6*s^5+15*n^4-60*n^3*s+90*n^2*s^2-60*n*s^3+15*s^4+20*n^3-60*n^2*s+60*n*s^2 -20*s^3+15*n^2-30*n*s+15*s^2+6*n-6*s+1)/(n^7+n^6*q-n^6*s+7*n^6+6*n^5*q-6*n^5*s+ 21*n^5+15*n^4*q-15*n^4*s+35*n^4+20*n^3*q-20*n^3*s+35*n^3+15*n^2*q-15*n^2*s+21*n ^2+6*n*q-6*n*s+7*n+q-s+1)*diff(diff(diff(diff(diff(diff(A[n+1](r,s),s),s),s),s) ,s),s) = 0 ------------------------------------------------- This took, 17.125, seconds.