The, 3, moment about the mean of the r.v. number of edges contained in the tr\ uth table of a random Boolean function is n 3 3 2 n ------- 64 and in Maple notation 3/64*2^n*n^3 hence the scaled, 3, moment is 2 1/2 6 n 2 ----------------------------- n 1/2 (2 n + 1) (n 2 (2 n + 1)) and in Maple notation 6*n^2*2^(1/2)/(2*n+1)/(n*2^n*(2*n+1))^(1/2) This took, 0.100, seconds. The, 4, moment about the mean of the r.v. number of edges contained in the tr\ uth table of a random Boolean function is n n 3 n 2 3 n 2 n 2 (12 2 n + 12 2 n + 40 n + 3 n 2 - 48 n + 12 n - 16) --------------------------------------------------------------- 1024 and in Maple notation 1/1024*n*2^n*(12*2^n*n^3+12*2^n*n^2+40*n^3+3*n*2^n-48*n^2+12*n-16) hence the scaled, 4, moment is 3 2 (-n) 3 (-n) 2 (-n) (-n) 12 n + 12 n + 40 2 n + 3 n - 48 2 n + 12 2 n - 16 2 ----------------------------------------------------------------------- 2 n (2 n + 1) and in Maple notation 1/n/(2*n+1)^2*(12*n^3+12*n^2+40*2^(-n)*n^3+3*n-48*2^(-n)*n^2+12*2^(-n)*n-16*2^( -n)) This took, 0.054, seconds. The, 5, moment about the mean of the r.v. number of edges contained in the tr\ uth table of a random Boolean function is n 3 n 2 n 2 5 2 n (6 2 n + 3 n 2 + 4 n - 24 n + 8) -------------------------------------------- 1024 and in Maple notation 5/1024*2^n*n^3*(6*2^n*n^2+3*n*2^n+4*n^2-24*n+8) hence the scaled, 5, moment is 20 n ( 2 1/2 1/2 (-n + 1/2) 2 (-n + 1/2) (-n + 1/2) 6 n 2 + 3 2 n + 4 2 n - 24 2 n + 8 2 ) / 2 n 1/2 / ((2 n + 1) (n 2 (2 n + 1)) ) / and in Maple notation 20*n/(2*n+1)^2/(n*2^n*(2*n+1))^(1/2)*(6*n^2*2^(1/2)+3*2^(1/2)*n+4*2^(-n+1/2)*n^ 2-24*2^(-n+1/2)*n+8*2^(-n+1/2)) This took, 1.164, seconds. The, 6, moment about the mean of the r.v. number of edges contained in the tr\ uth table of a random Boolean function is n n 2 5 n 2 4 n 5 n 2 3 n 4 n 2 (120 (2 ) n + 180 (2 ) n + 1920 2 n + 90 (2 ) n - 840 2 n 5 2 n 2 n 3 4 n 2 3 - 1792 n + 15 n (2 ) - 360 2 n - 5280 n - 300 2 n + 3840 n n 2 - 240 n 2 + 3840 n - 6720 n + 4864)/32768 and in Maple notation 1/32768*n*2^n*(120*(2^n)^2*n^5+180*(2^n)^2*n^4+1920*2^n*n^5+90*(2^n)^2*n^3-840* 2^n*n^4-1792*n^5+15*n^2*(2^n)^2-360*2^n*n^3-5280*n^4-300*2^n*n^2+3840*n^3-240*n *2^n+3840*n^2-6720*n+4864) hence the scaled, 6, moment is 5 4 (-n) 5 3 (-n) 4 (-n) 5 2 (120 n + 180 n + 1920 2 n + 90 n - 840 2 n - 1792 4 n + 15 n (-n) 3 (-n) 4 (-n) 2 (-n) 3 - 360 2 n - 5280 4 n - 300 2 n + 3840 4 n (-n) (-n) 2 (-n) (-n) / 2 - 240 2 n + 3840 4 n - 6720 4 n + 4864 4 ) / (n / 3 (2 n + 1) ) and in Maple notation 1/n^2/(2*n+1)^3*(120*n^5+180*n^4+1920*2^(-n)*n^5+90*n^3-840*2^(-n)*n^4-1792*4^( -n)*n^5+15*n^2-360*2^(-n)*n^3-5280*4^(-n)*n^4-300*2^(-n)*n^2+3840*4^(-n)*n^3-\ 240*2^(-n)*n+3840*4^(-n)*n^2-6720*4^(-n)*n+4864*4^(-n)) This took, 3629.001, seconds. This took, 3630.381, seconds .