A331484 Expansion of 1/(1 + x*Product_{k>=1} (1 - x^k)).

1, -1, 2, -2, 3, -3, 3, -2, -1, 5, -13, 22, -36, 51, -68, 82, -86, 75, -31, -52, 201, -421, 732, -1125, 1575, -2024, 2344, -2370, 1807, -327, -2532, 7210, -14128, 23486, -35027, 47799, -59594, 66717, -63246, 41012, 10696, -104335, 252653, -465825, 746343

Offset: 0

Author

Seiichi Manyama, Jan 18 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. similar sequences: A067687, A299105, A299106, A299208, A302017, A318581, A318582.

Cf. A010815.

Programs

Mathematica

m = 44; CoefficientList[Series[1/(1 + x*Product[1 - x^k, {k, 1, m}]), {x, 0, m}], x] (* Amiram Eldar, May 05 2021 *)

PARI

N=66; x='x+O('x^N); Vec(1/(1+x*prod(k=1, N, 1-x^k)))

Formula

a(0) = 1, a(n) = -Sum_{k=1..n} A010815(k-1)*a(n-k) for n > 0.