A261649 Expansion of Product_{k>=0} ((1+x^(3*k+1))/(1-x^(3*k+1)))^2.

1, 4, 8, 12, 20, 36, 56, 80, 120, 180, 252, 348, 492, 680, 912, 1228, 1652, 2180, 2856, 3744, 4860, 6256, 8044, 10284, 13048, 16520, 20848, 26140, 32672, 40756, 50596, 62576, 77256, 95060, 116540, 142592, 174036, 211736, 257056, 311448, 376332, 453764, 546160

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2015

Keywords

• nonn

Crossrefs

Cf. A015128, A156616, A080054, A007096, A261610, A261651.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[((1+x^(3*k+1))/(1-x^(3*k+1)))^2,{k,0,nmax}],{x,0,nmax}],x]

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) * Gamma(1/3)^2 / (2^(7/4) * 3^(5/12) * Pi^(4/3) * n^(7/12)).