A307626 Expansion of Product_{k>=1} 1/(1 - x^k/(1 + x)).

1, 1, 1, 1, 2, 1, 4, 0, 8, -3, 16, -12, 36, -40, 88, -117, 220, -321, 560, -860, 1447, -2284, 3772, -6032, 9861, -15864, 25798, -41627, 67527, -109132, 176826, -285985, 463089, -749189, 1212722, -1962181, 3175635, -5138421, 8315361, -13455103, 21772865

Offset: 0

Author

Seiichi Manyama, Apr 19 2019

Keywords

• sign

Links

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

Crossrefs

Convolution inverse A307601.

Cf. A227682.

Programs

Mathematica

m = 40; CoefficientList[Series[Product[1/(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(1/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)).