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

%I #13 Apr 14 2019 11:55:20

%S 1,-2,-2,-12,-90,-968,-12764,-200464,-3674378,-76958942,-1814783184,

%T -47618072204,-1376556963244,-43481881639608,-1490306874257184,

%U -55091497907730000,-2185104061817592618,-92567886910879671396,-4171638481112174023226

%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 25 2018

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

%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. A303306, A303344.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 22 2018