A279227 Expansion of Product_{k>=1} (1 + x^(k^2))^2/(1 - x^(k^2))^2.

1, 4, 8, 12, 20, 36, 56, 76, 104, 152, 216, 284, 364, 484, 648, 828, 1028, 1300, 1664, 2076, 2532, 3108, 3848, 4700, 5640, 6776, 8200, 9848, 11660, 13796, 16424, 19452, 22776, 26612, 31240, 36572, 42440, 49092, 56968, 66044, 76040, 87236, 100280, 115244

Offset: 0

Author

Vaclav Kotesovec, Dec 08 2016

Keywords

• nonn

Links

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

Crossrefs

Cf. A001156, A033461, A103265, A279225, A279226.

Programs

Mathematica

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

Formula

a(n) ~ (4-sqrt(2)) * Zeta(3/2) * exp(3 * Pi^(1/3) * ((4-sqrt(2)) * Zeta(3/2))^(2/3) * n^(1/3) / 2^(4/3)) / (32 * sqrt(3) * Pi^2 * n^(3/2)). - Vaclav Kotesovec, Dec 29 2016