A262953 - OEIS

A262953

Expansion of Product_{k>=1} (1 + x^(2*k-1)) * (1 + x^(3*k-2)).

1, 2, 1, 1, 3, 4, 3, 4, 7, 7, 8, 11, 13, 15, 18, 21, 25, 31, 34, 38, 48, 56, 61, 72, 85, 95, 109, 126, 142, 163, 186, 207, 237, 272, 301, 339, 389, 433, 482, 547, 612, 680, 764, 851, 946, 1061, 1177, 1301, 1455, 1616, 1779, 1977, 2194, 2415, 2670, 2953, 3250

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OFFSET

0,2

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) ~ 5^(1/4) * exp(Pi*sqrt(5*n/2)/3) / (2^(19/12) * sqrt(3) * n^(3/4)).

MATHEMATICA

nmax = 60; CoefficientList[Series[Product[(1 + x^(2*k-1)) * (1 + x^(3*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000700, A261612, A262952.