A285447 Expansion of Product_{k>=1} ((1 + x^(3*k)) / (1 - x^k))^k.

1, 1, 3, 7, 14, 27, 56, 101, 190, 347, 617, 1082, 1895, 3230, 5490, 9226, 15332, 25259, 41356, 67021, 107989, 172789, 274613, 433815, 681650, 1064661, 1654739, 2559029, 3938438, 6033967, 9205152, 13982675, 21156174, 31886290, 47879210, 71636483, 106814323

Offset: 0

Author

Vaclav Kotesovec, Apr 19 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A266648, A285446.

Cf. A156616, A285462, A285460, A285461.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[((1+x^(3*k))/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(1/12 + 2^(-4/3) * 3^(2/3) * (13*Zeta(3))^(1/3) * n^(2/3)) * (13*Zeta(3))^(7/36) / (A * 2^(7/9) * 3^(25/36) * sqrt(Pi) * n^(25/36)), where A is the Glaisher-Kinkelin constant A074962.