A293629 Expansion of Product_{k>0} ((1 - q^(3*k))^4*(1 - q^(6*k))^2)/((1 - q^k)^4*(1 - q^(2*k))^2).

1, 4, 16, 44, 122, 288, 672, 1432, 3005, 5960, 11632, 21836, 40376, 72568, 128640, 223112, 382192, 643404, 1071152, 1757968, 2856482, 4586000, 7296768, 11490912, 17949404, 27787684, 42702576, 65106188, 98599604, 148274760, 221611776, 329127848, 486057756

Offset: 0

Author

Seiichi Manyama, Oct 13 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A293426, A293628.

Cf. A293569.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1-x^(3*k))^4 * (1-x^(6*k))^2 / ((1-x^k)^4 * (1-x^(2*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 15 2017 *)

Formula

a(n) = (1/3) * A293569(3*n+2).

a(n) ~ 5^(1/4) * exp(2*Pi*sqrt(5*n)/3) / (2 * 3^(14/4)* n^(3/4)). - Vaclav Kotesovec, Oct 15 2017