A279411 Expansion of Product_{k>0} 1/(1 + x^k)^(k*4).

1, -4, 2, 0, 23, -20, 2, -88, 63, -96, 318, -104, 626, -844, 504, -2472, 1525, -3704, 6184, -4288, 15284, -10736, 23254, -35792, 30228, -84544, 60974, -139240, 176658, -190108, 418940, -320976, 755332, -773524, 1111678, -1847304, 1669046, -3634296

Offset: 0

Author

Seiichi Manyama, Apr 11 2017

Keywords

• sign

Links

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

Crossrefs

Column k=4 of A279928.

Product_{k>0} 1/(1 + x^k)^(k*m): A027906 (m=-4), A255528 (m=1), A278710 (m=2), A279031 (m=3), this sequence (m=4), A279932 (m=5).

Formula

a(n) ~ (-1)^n * exp(-1/3 + 3/2 * Zeta(3)^(1/3) * n^(2/3)) * A^4 * Zeta(3)^(1/18) / (sqrt(6*Pi) * n^(5/9)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 13 2017

G.f.: exp(4*Sum_{k>=1} (-1)^k*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, Mar 27 2018