A306749 Expansion of Product_{k>=1} 1/(1 - x^k * (1 - x)).

1, 1, 1, 0, 0, -1, 1, -1, 2, -2, 2, -4, 6, -8, 11, -13, 16, -23, 32, -44, 61, -80, 102, -133, 178, -243, 331, -441, 579, -759, 1001, -1335, 1792, -2398, 3186, -4205, 5537, -7320, 9734, -12975, 17266, -22893, 30267, -40004, 52968, -70282, 93348, -123900, 164179, -217277

Offset: 0

Author

Seiichi Manyama, Apr 16 2019

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A152398, A227681, A306691.

Programs

Mathematica

m = 49; 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)))

Formula

G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (1 - x)^d/d). - Ilya Gutkovskiy, Apr 16 2019