A278710 Convolution square of A255528.

1, -2, -1, -2, 7, 2, 10, -8, 5, -40, -4, -54, 52, -30, 162, -12, 292, -142, 270, -576, 168, -1228, 305, -1702, 1435, -1664, 3839, -1444, 7303, -2752, 10117, -8420, 11065, -20714, 11066, -38702, 17057, -57276, 40310, -69898, 94138, -77014, 181926, -97480

Offset: 0

Author

Seiichi Manyama, Apr 11 2017

Keywords

• sign

Links

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

Crossrefs

Product_{k>0} 1/(1 + x^k)^(k*m): A026011 (m=-2), A255528 (m=1), this sequence (m=2), A279031 (m=3), A279411 (m=4).

Formula

G.f.: Product_{k>0} 1/(1 + x^k)^(k*2).

a(n) ~ (-1)^n * exp(-1/6 + 3 * 2^(-4/3) * Zeta(3)^(1/3) * n^(2/3)) * A^2 * Zeta(3)^(1/9) / (2^(11/18) * sqrt(3*Pi) * n^(11/18)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 13 2017

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