A285294 Expansion of Product_{k>=1} (1 + x^(3*k))^(3*k) / (1 + x^k)^k.

1, -1, -1, 1, -2, -3, 7, -4, -1, 20, -9, -15, 45, -39, -38, 95, -81, -99, 244, -196, -188, 538, -371, -421, 1256, -823, -820, 2575, -1672, -1904, 5367, -3714, -3861, 10555, -7362, -8159, 21391, -14975, -15592, 41654, -28293, -30748, 82026, -54899, -57331, 155933

Offset: 0

Author

Seiichi Manyama, Apr 16 2017

Keywords

• sign

Links

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

Crossrefs

Product_{k>=1} (1 + x^(m*k))^(m*k) / (1 + x^k)^k: A284628 (m=2), this sequence (m=3), A285295 (m=4).

Cf. A262924.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1 + x^(3*k))^(3*k) / (1 + x^k)^k, {k,1,nmax}], {x,0,nmax}], x] (* Vaclav Kotesovec, Apr 16 2017 *)