A307601 Expansion of Product_{k>=1} (1 - x^k/(1 + x)).

1, -1, 0, 0, -1, 2, -4, 7, -11, 16, -21, 26, -30, 33, -33, 28, -14, -13, 59, -131, 238, -390, 598, -873, 1225, -1663, 2194, -2822, 3544, -4347, 5202, -6059, 6838, -7420, 7633, -7238, 5911, -3226, -1365, 8552, -19190, 34320, -55189, 83266, -120254, 168094, -228958

Offset: 0

Author

Seiichi Manyama, Apr 18 2019

Keywords

• sign
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A126348, A307599, A307602.

Programs

Mathematica

m = 46; CoefficientList[Series[Product[1 - x^k/(1 + x), {k, 1, m}], {x, 0, m}], x] (* Amiram Eldar, May 14 2021 *)

PARI

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

PARI

N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1+x)^d)))))

Formula

G.f.: exp(-Sum_{k>=1} x^k * Sum_{d|k} 1/(d*(1+x)^d)).