A038066 Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 5x.

5, -15, 40, -150, 624, -2620, 11160, -48750, 217000, -976872, 4438920, -20343700, 93900240, -435970980, 2034504992, -9536718750, 44878791360, -211927733500, 1003867701480, -4768371093720, 22706531339280

Offset: 1

Author

Christian G. Bower, Jan 04 1999

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane, Euler transform

Crossrefs

Cf. A038063, A038064, A038065, A038067, A038068, A038069, A038070.

Programs

PARI

x='x+O('x^22); Vec(sum(k=1, 22, moebius(k)*log(1 + 5*x^k)/k)) \\ Indranil Ghosh, May 24 2017

Formula

G.f.: Sum_{k>=1} mu(k)*log(1 + 5*x^k)/k. - Ilya Gutkovskiy, May 23 2017

a(n) ~ -(-1)^n * 5^n / n. - Vaclav Kotesovec, Jun 12 2018

a(n) = -(1/n) * Sum_{d|n} mu(n/d) * (-5)^d. - Seiichi Manyama, Apr 12 2025