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Expansion of Product_{k>0} ((1 - q^(3*k))^4*(1 - q^(6*k))^2)/((1 - q^k)^4*(1 - q^(2*k))^2).
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%I #13 Oct 15 2017 05:34:39

%S 1,4,16,44,122,288,672,1432,3005,5960,11632,21836,40376,72568,128640,

%T 223112,382192,643404,1071152,1757968,2856482,4586000,7296768,

%U 11490912,17949404,27787684,42702576,65106188,98599604,148274760,221611776,329127848,486057756

%N Expansion of Product_{k>0} ((1 - q^(3*k))^4*(1 - q^(6*k))^2)/((1 - q^k)^4*(1 - q^(2*k))^2).

%H Seiichi Manyama, <a href="/A293629/b293629.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = (1/3) * A293569(3*n+2).

%F a(n) ~ 5^(1/4) * exp(2*Pi*sqrt(5*n)/3) / (2 * 3^(14/4)* n^(3/4)). - _Vaclav Kotesovec_, Oct 15 2017

%t nmax = 50; CoefficientList[Series[Product[(1-x^(3*k))^4 * (1-x^(6*k))^2 / ((1-x^k)^4 * (1-x^(2*k))^2), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 15 2017 *)

%Y Cf. A293426, A293628.

%Y Cf. A293569.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 13 2017