A285988 Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^(n^2) in powers of x.

1, -2, -6, -4, 22, 72, 92, -48, -522, -1294, -1624, 300, 6948, 19032, 30192, 20432, -45578, -202788, -437178, -599460, -311112, 1038624, 4023532, 8423280, 11892004, 8429270, -12073032, -60747944, -139842736, -223644552, -232762256, -15050944, 636838518

Offset: 0

Author

Seiichi Manyama, Apr 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Product_{n>0} ((1-x^n)/(1+x^n))^(n^m): A002448 (m=0), A285675 (m=1), this sequence (m=2), A285990 (m=3), A285991 (m=4).

Cf. A007331, A206622.

Formula

a(0) = 1, a(n) = -(2/n)*Sum_{k=1..n} A007331(k)*a(n-k) for n > 0.

G.f.: exp(Sum_{k>=1} (sigma_3(k) - sigma_3(2*k))*x^k/(4*k)). - Ilya Gutkovskiy, Apr 14 2019