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%I A262883 #12 Oct 06 2015 07:20:21
%S A262883 1,1,2,2,5,7,10,15,24,33,49,68,100,136,193,267,370,501,690,928,1260,
%T A262883 1687,2265,3007,4006,5289,6987,9163,12033,15698,20469,26572,34470,
%U A262883 44510,57442,73861,94852,121439,155287,198007,252165,320335,406396,514410,650288
%N A262883 Expansion of Product_{k>=1} 1/((1-x^(3*k-1))*(1-x^(3*k-2)))^k.
%C A262883 Convolution of A262876 and A262877.
%H A262883 Vaclav Kotesovec and Alois P. Heinz, <a href="/A262883/b262883.txt">Table of n, a(n) for n = 0..10000</a> (first 2001 terms from Vaclav Kotesovec)
%H A262883 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015
%F A262883 a(n) ~ exp(-1/18 - Pi^4/(864*Zeta(3)) + (3*Zeta(3)/2)^(1/3) * n^(2/3) + Pi^2 * n^(1/3) / (2^(5/3)*3^(4/3)*Zeta(3)^(1/3))) * A^(2/3) * Gamma(4/3)^(1/3) * Zeta(3)^(7/54) / (2^(11/27) * 3^(79/108) * Pi^(2/3) * n^(17/27)), where Zeta(3) = A002117 and A = A074962 is the Glaisher-Kinkelin constant.
%p A262883 with(numtheory):
%p A262883 a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p A262883       `if`(irem(d+3, 3, 'r')=0, 0, r), d=divisors(j))*a(n-j), j=1..n)/n)
%p A262883     end:
%p A262883 seq(a(n), n=0..60);  # _Alois P. Heinz_, Oct 05 2015
%t A262883 nmax = 50; CoefficientList[Series[Product[1/((1-x^(3*k-1))*(1-x^(3*k-2)))^k, {k, 1, nmax}], {x, 0, nmax}], x]
%Y A262883 Cf. A262876, A262877, A262884, A262923.
%K A262883 nonn
%O A262883 0,3
%A A262883 _Vaclav Kotesovec_, Oct 04 2015

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