A285292 Expansion of Product_{k>=1} (1 + x^k)^k / (1 + x^(4*k))^(4*k).

1, 1, 2, 5, 4, 12, 20, 29, 53, 80, 127, 199, 311, 468, 715, 1079, 1621, 2402, 3541, 5210, 7574, 11046, 15926, 22917, 32804, 46766, 66419, 93936, 132331, 185830, 260144, 362752, 504573, 699376, 966842, 1332721, 1832217, 2512209, 3435932, 4687884, 6380911

Offset: 0

Author

Vaclav Kotesovec, Apr 16 2017

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)

Crossrefs

Cf. A262736, A262924, A285293.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k)^k/(1+x^(4*k))^(4*k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(3^(5/3) * Zeta(3)^(1/3) * n^(2/3) / 4) * Zeta(3)^(1/6) / (2^(3/4) * 3^(1/6) * sqrt(Pi) * n^(2/3)).