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Expansion of Product_{k>0} (1 - q^(3*k))^5/((1 - q^k)^3*(1 - q^(6*k))^2).
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%I #14 Oct 09 2017 08:26:16

%S 1,3,9,17,36,63,118,195,333,528,852,1305,2020,3012,4518,6583,9624,

%T 13761,19698,27702,38952,54000,74784,102357,139882,189297,255690,

%U 342497,457824,607617,804656,1058970,1390545,1815984,2366268,3068388,3970008,5114382,6574266

%N Expansion of Product_{k>0} (1 - q^(3*k))^5/((1 - q^k)^3*(1 - q^(6*k))^2).

%H Seiichi Manyama, <a href="/A293423/b293423.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ 5^(1/4) * exp(sqrt(10*n)*Pi/3) / (9*2^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Oct 09 2017

%t nmax = 50; CoefficientList[Series[Product[(1 - x^(3*k))^5 / ((1 - x^k)^3 * (1 - x^(6*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 09 2017 *)

%Y Cf. A293421.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 08 2017