A262667 Expansion of Product_{k>=1} (1+x^k)^k / (1-x^k).

1, 2, 5, 12, 25, 52, 103, 198, 370, 680, 1221, 2158, 3757, 6448, 10931, 18322, 30382, 49894, 81206, 131044, 209818, 333466, 526294, 825182, 1285807, 1991754, 3068074, 4700910, 7166216, 10871534, 16416358, 24679224, 36943232, 55075758, 81785488, 120989244

Offset: 0

Author

Vaclav Kotesovec, Oct 03 2015

Keywords

• nonn

Comments

Convolution of A026007 and A000041.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
• Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015

Crossrefs

Cf. A026007, A000041, A262803.

Programs

Mathematica

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

Formula

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(4/3) + Pi^2 * n^(1/3)/(2^(2/3) * 3^(4/3) * Zeta(3)^(1/3)) - Pi^4 / (324*Zeta(3))) * Zeta(3)^(1/3) / (2^(17/12) * 3^(1/6) * Pi * n^(5/6)).