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A027346 Expansion of Product_{m>=1} (1 + q^m)^(3*m). 9
1, 3, 9, 28, 72, 183, 443, 1026, 2313, 5072, 10860, 22767, 46862, 94806, 188886, 371068, 719493, 1378449, 2611540, 4896291, 9090651, 16723930, 30501744, 55177932, 99048719, 176500572, 312330813, 549033172 (list; graph; refs; listen; history; text; internal format)
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) ~ exp(2^(-4/3) * 3^(5/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(11/12) * 3^(1/6) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Aug 17 2015

G.f.: exp(3*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)^(3*k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 17 2015 *)

CROSSREFS

Column k=3 of A277938.

Cf. A026007, A026011, A027906.

Sequence in context: A026524 A282081 A022631 * A294958 A047134 A184698

Adjacent sequences:  A027343 A027344 A027345 * A027347 A027348 A027349

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 16 09:23 EST 2019. Contains 320161 sequences. (Running on oeis4.)