A359936 Expansion of Product_{k>=0} (1 - x^(k^2+1)) in powers of x.
1, -1, -1, 1, 0, -1, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, -1, -2, 2, 1, -1, 0, 1, -1, -1, 1, -1, 2, 0, -2, 1, 1, -2, 0, 2, -1, 1, -2, 0, 2, -1, -1, 2, 1, -3, 0, 1, 1, -2, 0, 1, 0, 0, -1, 3, 0, -3, 0, 2, -2, 1, 1, -2, 2, -2, -2, 4, 2, -4, 1, 2, -3, -1, 1, 2, 1, -1, -3, 2
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
-
PARI
my(N=100, x='x+O('x^N)); Vec(prod(k=0, sqrtint(N), 1-x^(k^2+1))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, sumdiv(j, d, issquare(d-1)*d)*v[i-j+1])/i); v;
Formula
a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A359937(k) * a(n-k).