A284474 Expansion of Product_{k>=1} (1 + x^(2*k))^(2*k)/(1 + x^(2*k-1))^(2*k-1).

1, -1, 3, -6, 11, -22, 42, -74, 131, -231, 395, -669, 1122, -1851, 3029, -4915, 7891, -12572, 19881, -31203, 48657, -75391, 116096, -177792, 270822, -410394, 618905, -929052, 1388403, -2066140, 3062270, -4520912, 6649463, -9745072, 14232278, -20716355, 30057438

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

Formula

a(n) ~ (-1)^n * exp(-1/12 + 3 * 2^(-5/3) * (7*Zeta(3))^(1/3) * n^(2/3)) * A * (7*Zeta(3))^(5/36) / (2^(10/9) * sqrt(3*Pi) * n^(23/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 17 2017

G.f.: exp(Sum_{k>=1} (-1)^k*x^k/(k*(1 + x^k)^2)). - Ilya Gutkovskiy, Jun 20 2018

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k))^(2*k)/(1 + x^(2*k-1))^(2*k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 15 2017 *)

Crossrefs

Cf. A026011, A281781, A284467, A284628.

Sequence in context: A195734 A018177 A103322 * A117075 A024506 A068033

Adjacent sequences: A284471 A284472 A284473 * A284475 A284476 A284477

Keyword

sign

Author

Seiichi Manyama, Apr 15 2017

Status

approved