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%I #7 Jan 10 2017 13:57:05
%S 1,2,3,6,10,16,25,38,56,82,118,166,233,322,440,598,804,1072,1422,1872,
%T 2449,3188,4126,5312,6810,8690,11040,13974,17618,22130,27707,34572,
%U 43000,53328,65942,81312,100004,122674,150110,183254,223200,271248,328945,398086
%N Expansion of Product_{k>=1} ((1+x^k) / ((1-x^(2*k-1)) * (1-x^(8*k-4)))).
%D G. E. Andrews and B. C. Berndt, Ramanujan’s Lost Notebook Part II, Springer, 2009. [Entry 1.7.5]
%H Vaclav Kotesovec, <a href="/A280908/b280908.txt">Table of n, a(n) for n = 0..2000</a>
%H Andrew Sills, <a href="https://works.bepress.com/andrew_sills/40/">Rademacher-Type Formulas for Restricted Partition and Overpartition Functions</a>, Ramanujan Journal, 23 (1-3): 253-264, 2010.
%F a(n) ~ sqrt(3)*Pi * BesselI(1, sqrt(12*n+3)*Pi/4) / (4*sqrt(8*n+2)).
%F a(n) ~ 3^(1/4) * exp(sqrt(3*n)*Pi/2) / (8*sqrt(2)*n^(3/4)) * (1 + (Pi/16 - 1/(4*Pi))*sqrt(3/n) + (3*Pi^2/512 - 5/(32*Pi^2) - 15/64)/n).
%t nmax = 50; CoefficientList[Series[Product[(1+x^k) / ((1-x^(2*k-1)) * (1-x^(8*k-4))), {k, 1, nmax}], {x, 0, nmax}], x]
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jan 10 2017