A359966 Expansion of Product_{k>=2} (1 - x^(k^2-1)) in powers of x.

1, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 1, 1, 0, 0, -1, 1, 0, 0, -1, -1, -1, 0, 2, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 0, 0, 1, 0, 1, 0, -1, -1, 0, 1, 1, 0, -2, -1, 1, 3

Offset: 0

Author

Seiichi Manyama, Jan 20 2023

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005563, A276516, A359936, A359967.

Programs

PARI

my(N=100, x='x+O('x^N)); Vec(prod(k=2, sqrtint(N+1), 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} A359967(k) * a(n-k).