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A279031
Expansion of Product_{k>0} 1/(1 + x^k)^(k*3).
6
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
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
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 11 2017
STATUS
approved