A285069 Expansion of Product_{k>=1} (1 - x^(2*k-1))^(2*k-1).

1, -1, 0, -3, 3, -5, 8, -10, 22, -25, 41, -57, 88, -126, 168, -261, 351, -512, 685, -984, 1357, -1865, 2566, -3485, 4838, -6459, 8832, -11831, 16056, -21404, 28660, -38259, 50875, -67613, 89161, -118184, 155321, -204609, 267708, -351125, 458331, -597740

Offset: 0

Author

Seiichi Manyama, Apr 09 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A050999, A262736, A262811.

Programs

Mathematica

CoefficientList[Series[Product[(1 - x^(2k-1))^(2k-1), {k, 50}], {x, 0, 50}], x] (* Indranil Ghosh, Apr 09 2017 *)

PARI

N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, sumdiv(k, d, d^2*(d%2))*x^k/k))) \\ Seiichi Manyama, Oct 31 2017

Formula

a(n) = (-1)^n * A262736(n).

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A050999(k)*a(n-k) for n > 0.

a(n) ~ (-1)^n * exp(3^(4/3) * (Zeta(3))^(1/3) * n^(2/3) / 2^(5/3)) * Zeta(3)^(1/6) / (2^(3/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Nov 09 2017