A263346 - OEIS

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A263346

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

1, 1, 3, 5, 12, 21, 40, 71, 130, 221, 387, 648, 1095, 1800, 2964, 4792, 7730, 12301, 19510, 30619, 47859, 74179, 114469, 175427, 267684, 406039, 613325, 921671, 1379500, 2055313, 3050652, 4509385, 6641966, 9746452, 14254242, 20775255, 30184451, 43715711

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

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

FORMULA

a(n) ~ 2^(1/6) * Zeta(3)^(1/6) * exp(6^(1/3) * Zeta(3)^(1/3) * n^(2/3)) / (3^(11/12) * sqrt(Pi) * n^(2/3)).

MATHEMATICA

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

CROSSREFS

Cf. A000726, A000219, A262876, A262877, A262878, A262879, A263345.