A285990 Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^(n^3) in powers of x.

1, -2, -14, -24, 78, 536, 1236, -308, -12322, -45218, -73680, 76144, 872868, 2833904, 4612952, -2467592, -42205746, -147191388, -285572658, -127256088, 1376616024, 6138841704, 14949184532, 19201535108, -18287313476, -186761626394, -604980766280

Offset: 0

Author

Seiichi Manyama, Apr 30 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..5987

Crossrefs

Product_{n>0} ((1-x^n)/(1+x^n))^(n^m): A002448 (m=0), A285675 (m=1), A285988 (m=2), this sequence (m=3), A285991 (m=4).

Cf. A206623, A285989.

Formula

a(0) = 1, a(n) = -(2/n)*Sum_{k=1..n} A285989(k)*a(n-k) for n > 0.

G.f.: exp(Sum_{k>=1} (sigma_4(k) - sigma_4(2*k))*x^k/(8*k)). - Ilya Gutkovskiy, Apr 14 2019