#hw3SalmanManzoor.txt

NuCGx:=proc(n,x) local f,z,i:

f:=log(add((1+x)^binomial(i,2)*z^i/i!,i=0..n)):
f:=taylor(f,z=0,n+1):
[seq( collect(i!*coeff(f,z,i),x),i=1..n)]:
end:

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

#NuCGk(n,0) yields OEIS A000272
#NuCGk(n,0) yields OEIS A057500
#The largest k for which NuCGk(n,k) is k=12 yielding A182371