#Please do not post homework
#James Betti, 2 Feb 2025, Assignment 3

PC := proc(n,p,K) local i:
    evalf(coeff(add(IsCo(RG(n,p)),i=1..K),true,1)/K);
end:

NuCCc := proc(n) local f,i:
    f := log(Sum(2^(i*(i-1)/2)*z^i/i!,i=0..infinity));
    f := taylor(f,z,n+1);
    [seq(i!*coeff(f,z,i),i=1..n)];
end:

NuCGx := proc(n,x) local f,i:
    f := log(Sum((1+x)^(i*(i-1)/2)*z^i/i!,i=0..infinity));
    f := taylor(f,z,n+1);
    [seq(i!*coeff(f,z,i),i=1..n)];
end:

NuCGk := proc(n,k) local F,i:
    F := NuCGx(n, x);
    [seq(coeff(F[i],x,i-1+k),i=1..n)];
end:

# k=0..12 are all in OEIS!
NuCGk(10,0);                            # A274391
NuCGk(10,1);                            # A057500
NuCGk(10,2);                            # A061540
NuCGk(10,3);                            # A061541
NuCGk(10,4);                            # A061542
NuCGk(10,5);                            # A061543
NuCGk(10,6);                            # A096117
NuCGk(10,7);                            # A061544
NuCGk(10,8);                            # A096150
NuCGk(10,9);                            # A096224
NuCGk(10,10);                           # A182294
NuCGk(10,11);                           # A182295
NuCGk(10,12);                           # A182371
NuCGk(10,13);                           # no match