A303344 Expansion of Product_{n>=1} ((1 + (n*x)^n)/(1 - (n*x)^n))^(1/n).

1, 2, 6, 28, 182, 1640, 19220, 278224, 4809942, 96598622, 2208156512, 56580566908, 1605518324884, 49963000166616, 1691615823420800, 61897541544248720, 2433873670903995990, 102341746590575878628, 4582360425862350559350, 217661837260679635780356

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• nonn

Crossrefs

Cf. A023881, A186633, A303307, A303343.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[((1 + (k*x)^k)/(1 - (k*x)^k))^(1/k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 22 2018 *)

PARI

N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+(k*x)^k)/(1-(k*x)^k))^(1/k)))

Formula

a(n) ~ 2 * n^(n-1). - Vaclav Kotesovec, Apr 22 2018

G.f.: exp(Sum_{k>=1} (sigma_k(2*k) - sigma_k(k))*x^k/(2^(k-1)*k)). - Ilya Gutkovskiy, Apr 14 2019