A307599 Expansion of Product_{k>=1} (1 - x^k/(1 - x)).

1, -1, -2, -2, -1, 2, 6, 11, 15, 16, 11, -2, -26, -61, -105, -152, -192, -209, -183, -89, 98, 400, 830, 1385, 2035, 2715, 3314, 3668, 3556, 2703, 790, -2521, -7550, -14542, -23591, -34546, -46901, -59670, -71261, -79358, -80830, -71690, -47133, -1684, 70504, 175168, 317232

Offset: 0

Author

Seiichi Manyama, Apr 17 2019

Keywords

• sign

Links

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

Crossrefs

Convolution inverse of A227682.

Cf. A126348, A307601, 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)).