A026011 Expansion of Product_{m>=1} (1 + q^m)^(2*m).

1, 2, 5, 14, 30, 68, 145, 298, 600, 1182, 2280, 4318, 8064, 14824, 26917, 48292, 85675, 150466, 261762, 451328, 771739, 1309362, 2205109, 3687904, 6127155, 10116074, 16602508, 27093582, 43974355, 71003224

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)

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, p. 19.

Formula

a(n) ~ Zeta(3)^(1/6) * exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3)/2) / (2^(2/3) * 3^(1/3) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Aug 17 2015

G.f.: exp(2*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)). - Ilya Gutkovskiy, May 30 2018

Mathematica

nmax = 40; CoefficientList[Series[Product[(1+x^k)^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 17 2015 *)

Crossrefs

Column k=2 of A277938.

Cf. A026007, A027346, A027906.

Sequence in context: A047133 A031874 A120328 * A212393 A056358 A336229

Adjacent sequences: A026008 A026009 A026010 * A026012 A026013 A026014

Keyword

nonn

Author

N. J. A. Sloane

Status

approved