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

Author

Seiichi Manyama, Jan 19 2023

Keywords

• sign
• look

Links

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

Crossrefs

Cf. A002522, A081362, A276516, A284312, A284313, A284314, A284585, A284499, A357911, A359937.

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).