A285675 Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^n in powers of x.

1, -2, -2, 0, 6, 8, 4, -4, -18, -34, -32, -8, 36, 96, 144, 152, 94, -60, -294, -560, -760, -760, -460, 228, 1276, 2486, 3576, 4080, 3456, 1304, -2576, -7956, -13986, -19208, -21644, -19056, -9462, 8200, 33364, 63224, 92384, 112860, 114976, 88896, 26660, -74792

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), this sequence (m=1), A285988 (m=2), A285990 (m=3), A285991 (m=4).

Cf. A076577, A156616.

Formula

a(0) = 1, a(n) = -(2/n)*Sum_{k=1..n} A076577(k)*a(n-k) for n > 0.

G.f.: exp(Sum_{k>=1} (sigma_2(k) - sigma_2(2*k))*x^k/(2*k)). - Ilya Gutkovskiy, Apr 14 2019

G.f.: exp( - 2*Sum_{n >= 0} x^(2*n+1)/((2*n+1)*(1 - x^(2*n+1))^2) ). Cf. A000122. - Peter Bala, Dec 23 2021