A291655 Expansion of Product_{k>=1} 1/(1-x^(k^2))^(k^2).

1, 1, 1, 1, 5, 5, 5, 5, 15, 24, 24, 24, 44, 80, 80, 80, 131, 221, 266, 266, 386, 566, 746, 746, 990, 1474, 1924, 2089, 2529, 3709, 4609, 5269, 6130, 8576, 11096, 12746, 14937, 19397, 25697, 28997, 34111, 43135, 56365, 65905, 76219, 95770, 120070, 144370, 163661

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A001156, A033461, A281790, A285047, A291649, A291696, A291720.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1-x^(k^2))^(k^2), {k,1,nmax}], {x,0,nmax}], x]

Formula

log(a(n)) ~ 5 * Pi^(1/5) * Zeta(5/2)^(2/5) * n^(3/5) / (2^(6/5) * 3^(3/5)).