A279031 Expansion of Product_{k>0} 1/(1 + x^k)^(k*3).

1, -3, 0, -1, 15, -3, 8, -42, 6, -83, 81, -39, 316, -90, 420, -603, 363, -1656, 625, -2556, 2877, -2599, 7818, -3483, 13886, -11049, 17040, -31493, 20196, -63876, 39244, -96453, 105891, -120431, 243333, -164100, 440873, -327387, 643968, -765115, 840207

Offset

0,2

Links

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

Formula

a(n) ~ (-1)^n * exp(-1/4 + 2^(-5/3) * 3^(4/3) * Zeta(3)^(1/3) * n^(2/3)) * A^3 * Zeta(3)^(1/12) / (2^(2/3) * 3^(5/12) * sqrt(Pi) * n^(7/12)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 13 2017

G.f.: exp(3*Sum_{k>=1} (-1)^k*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, Mar 27 2018

Crossrefs

Product_{k>0} 1/(1 + x^k)^(k*m): A027346 (m=-3), A255528 (m=1), A278710 (m=2), this sequence (m=3), A279411 (m=4).

Sequence in context: A368054 A289546 A334823 * A304336 A287315 A350212

Adjacent sequences: A279028 A279029 A279030 * A279032 A279033 A279034

Keyword

sign

Author

Seiichi Manyama, Apr 11 2017

Status

approved