A303343 Expansion of Product_{n>=1} ((1 - (n*x)^n)/(1 + (n*x)^n))^(1/n).

1, -2, -2, -12, -90, -968, -12764, -200464, -3674378, -76958942, -1814783184, -47618072204, -1376556963244, -43481881639608, -1490306874257184, -55091497907730000, -2185104061817592618, -92567886910879671396, -4171638481112174023226

Offset: 0

Author

Seiichi Manyama, Apr 22 2018

Keywords

• sign

Crossrefs

Cf. A303306, A303344.

Programs

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 25 2018

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