A291666 Expansion of Product_{k>=1} ((1 + x^(k^2)) / (1 - x^(k^2)))^(k^2).

1, 2, 2, 2, 10, 18, 18, 18, 50, 100, 118, 118, 206, 438, 582, 582, 806, 1606, 2344, 2506, 3122, 5322, 8202, 9498, 11130, 16844, 26110, 32272, 37018, 52274, 78018, 100098, 115986, 155026, 223190, 291674, 345132, 439518, 618734, 811790, 972846, 1204190, 1653726

Offset: 0

Author

Vaclav Kotesovec, Aug 29 2017

Keywords

• nonn

Comments

Convolution of A291649 and A291655.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001156, A033461, A103265, A156616, A206622, A291649, A291655, A291667, A291721.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^(k^2))/(1-x^(k^2)))^(k^2), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

log(a(n)) ~ 5 * Pi^(1/5) * ((8-sqrt(2)) * Zeta(5/2))^(2/5) * n^(3/5) / (4*3^(3/5)).