A291667 Expansion of Product_{k>=1} ((1 + x^(k^2)) / (1 - x^(k^2)))^k.

1, 2, 2, 2, 6, 10, 10, 10, 18, 32, 38, 38, 50, 86, 110, 110, 134, 206, 272, 290, 342, 466, 610, 682, 770, 1012, 1310, 1492, 1654, 2130, 2698, 3066, 3410, 4210, 5310, 6106, 6812, 8078, 10118, 11750, 13006, 15198, 18654, 21810, 24178, 28092, 33682, 39330, 43866

Offset: 0

Author

Vaclav Kotesovec, Aug 29 2017

Keywords

• nonn

Comments

Convolution of A285047 and A281790.

Links

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

Crossrefs

Cf. A001156, A033461, A285047, A281790, A291666.

Programs

Mathematica

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

Formula

log(a(n)) ~ Pi*sqrt(n/2).