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

0,2

Links

Table of n, a(n) for n=0..18.

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

Prog

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

Crossrefs

Cf. A303306, A303344.

Sequence in context: A013315 A032321 A013311 * A087220 A032320 A032227

Adjacent sequences: A303340 A303341 A303342 * A303344 A303345 A303346

Keyword

sign

Author

Seiichi Manyama, Apr 22 2018

Status

approved