A261451 Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(k+1).

1, 4, 14, 44, 124, 328, 824, 1980, 4590, 10320, 22584, 48268, 101016, 207432, 418704, 832032, 1629764, 3150280, 6014998, 11354084, 21204488, 39206168, 71811256, 130369900, 234704360, 419195412, 743085912, 1307823672, 2286094704, 3970174648, 6852048368

Offset: 0

Author

Vaclav Kotesovec, Aug 19 2015

Keywords

• nonn

Comments

Convolution of A005380 and A219555.

Links

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

Crossrefs

Cf. A156616, A005309, A261386, A261452, A261389.

Programs

Mathematica

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

Formula

a(n) ~ (7*Zeta(3))^(13/36) * exp(1/12 - Pi^4/(336*Zeta(3)) + Pi^2 * n^(1/3) / (2^(5/3) * (7*Zeta(3))^(1/3)) + 3/2 * ((7*Zeta(3))/2)^(1/3) * n^(2/3)) / (A * 2^(35/18) * 3^(1/2) * Pi * n^(31/36)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.