A038065 Product_{k>=1} 1/(1 - x^k)^a(k) = 1 + 4x.

4, -10, 20, -60, 204, -690, 2340, -8160, 29120, -104958, 381300, -1397740, 5162220, -19175130, 71582716, -268431360, 1010580540, -3817763040, 14467258260, -54975528948, 209430785460, -799645010850, 3059510616420

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, A038066, A038067, A038068, A038069, A038070.

Programs

PARI

x='x+O('x^24); Vec(sum(k=1, 24, moebius(k)*log(1 + 4*x^k)/k)) \\ Indranil Ghosh, May 24 2017

Formula

G.f.: Sum_{k>=1} mu(k)*log(1 + 4*x^k)/k. - Ilya Gutkovskiy, May 23 2017

a(n) ~ -(-1)^n * 4^n / n. - Vaclav Kotesovec, Jun 12 2018

a(n) = -(1/n) * Sum_{d|n} mu(n/d) * (-4)^d. - Seiichi Manyama, Apr 12 2025