A285991 Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^(n^4) in powers of x.

1, -2, -30, -100, 262, 3672, 13836, -80, -264810, -1421438, -3019032, 7630764, 89648580, 358974280, 548677872, -2390377936, -20531491146, -74635378020, -110275527170, 425036176572, 3669041188152, 13597190512480, 23995331740700, -45340748171760

Offset: 0

Author

Seiichi Manyama, Apr 30 2017

Keywords

• sign

Crossrefs

Product_{n>0} ((1-x^n)/(1+x^n))^(n^m): A002448 (m=0), A285675 (m=1), A285988 (m=2), A285990 (m=3), this sequence (m=4).

Cf. A096960, A206624.

Formula

a(0) = 1, a(n) = -(2/n)*Sum_{k=1..n} A096960(k)*a(n-k) for n > 0.

G.f.: exp(Sum_{k>=1} (sigma_5(k) - sigma_5(2*k))*x^k/(16*k)). - Ilya Gutkovskiy, Apr 14 2019