A261650 Expansion of Product_{k>=0} ((1+x^(4*k+1))/(1-x^(4*k+1)))^2.

1, 4, 8, 12, 16, 24, 40, 60, 80, 104, 144, 204, 272, 344, 440, 584, 768, 968, 1200, 1516, 1936, 2424, 2968, 3644, 4528, 5596, 6800, 8216, 10000, 12184, 14688, 17564, 21056, 25320, 30272, 35912, 42576, 50616, 60024, 70728, 83136, 97896, 115200, 134924, 157504

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2015

Keywords

• nonn

Crossrefs

Cf. A015128, A156616, A080054, A007096, A261611, A261652.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[((1+x^(4*k+1))/(1-x^(4*k+1)))^2,{k,0,nmax}],{x,0,nmax}],x]

Formula

a(n) ~ exp(Pi*sqrt(n/2)) * 2^(3/2) * Gamma(1/4)^2 / (16 * Pi^(3/2) * sqrt(n)).