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%I #7 Jan 12 2017 12:50:58
%S 1,0,2,1,4,2,7,4,12,8,20,14,32,24,50,39,76,62,114,96,168,145,244,216,
%T 350,316,496,456,696,650,968,916,1334,1278,1824,1766,2475,2420,3336,
%U 3290,4468,4440,5948,5952,7874,7929,10368,10500,13584,13828,17714
%N Expansion of Product_{k>=1} (1 - x^(6*k)) * (1 + x^(12*k-3)) * (1 + x^(12*k-9)) / ((1 - x^(4*k-2)) * (1 - x^(2*k))).
%H Vaclav Kotesovec, <a href="/A280948/b280948.txt">Table of n, a(n) for n = 0..10000</a>
%H Andrew Sills, <a href="http://home.dimacs.rutgers.edu/~asills/EMDC/SillsEMDC-Rev.pdf">Towards an Automation of the Circle Method</a>, Gems in Experimental Mathematics in Contemporary Mathematics, 2010, formula S107.
%F a(n) ~ 2*Pi * BesselI(1, sqrt(8*n+1)*Pi/(3*sqrt(2))) / (3*sqrt(24*n+3)).
%F a(n) ~ exp(2*Pi*sqrt(n)/3) / (3*2^(3/2)*n^(3/4)) * (1 + (Pi/24 - 9/(16*Pi))/sqrt(n) + (Pi^2/1152 - 135/(512*Pi^2) - 15/128)/n).
%t nmax=50; CoefficientList[Series[Product[(1-x^(6*k))*(1+x^(12*k-3))*(1+x^(12*k-9))/((1-x^(4*k-2))*(1-x^(2*k))), {k, 1, nmax}], {x, 0, nmax}], x]
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jan 11 2017
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