A360001 Expansion of Product_{k>=0} (1 - x^(k^2+4)) in powers of x.

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

Offset: 0

Author

Seiichi Manyama, Jan 21 2023

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A276516, A359936, A359966, A359980, A360002, A360003.

Programs

PARI

my(N=100, x='x+O('x^N)); Vec(prod(k=0, sqrtint(N), 1-x^(k^2+4)))

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-4)*d)*v[i-j+1])/i); v;