A278668 Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3 in powers of x.

1, 3, 9, 22, 51, 107, 218, 420, 788, 1428, 2531, 4375, 7430, 12377, 20313, 32833, 52402, 82585, 128750, 198588, 303428, 459375, 689710, 1027243, 1518709, 2229375, 3251022, 4710777, 6785378, 9717677, 13841991, 19614182, 27656250, 38810312, 54216128, 75406438

Offset: 0

Author

Seiichi Manyama, Nov 25 2016

Keywords

• nonn

Examples

			G.f.: 1 + 3*x + 9*x^2 + 22*x^3 + 51*x^4 + 107*x^5 + 218*x^6 + ...
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^k: A035959 (k=1), A160461 (k=2), this sequence (k=3), A278680 (k=4), A277212 (k=5), A182821 (k=6).

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 10 2017 *)

Formula

G.f.: Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^3.

a(n) ~ exp(2*Pi*sqrt(7*n/15)) * 7^(3/4) / (20 * 3^(3/4) * 5^(1/4) * n^(5/4)). - Vaclav Kotesovec, Nov 10 2017