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%I #15 Apr 14 2019 11:55:26
%S 1,2,6,28,182,1640,19220,278224,4809942,96598622,2208156512,
%T 56580566908,1605518324884,49963000166616,1691615823420800,
%U 61897541544248720,2433873670903995990,102341746590575878628,4582360425862350559350,217661837260679635780356
%N Expansion of Product_{n>=1} ((1 + (n*x)^n)/(1 - (n*x)^n))^(1/n).
%F a(n) ~ 2 * n^(n-1). - _Vaclav Kotesovec_, Apr 22 2018
%F G.f.: exp(Sum_{k>=1} (sigma_k(2*k) - sigma_k(k))*x^k/(2^(k-1)*k)). - _Ilya Gutkovskiy_, Apr 14 2019
%t 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 *)
%o (PARI) N=66; x='x+O('x^N); Vec(prod(k=1, N, ((1+(k*x)^k)/(1-(k*x)^k))^(1/k)))
%Y Cf. A023881, A186633, A303307, A303343.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 22 2018
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