%I #10 Jan 10 2017 04:59:07

%S 1,1,1,0,1,2,1,1,2,3,2,1,3,4,2,3,5,6,4,3,7,9,6,6,9,12,9,7,13,16,12,11,

%T 18,22,17,15,23,29,22,21,32,38,31,27,41,49,39,37,54,63,52,48,68,80,66,

%U 64,88,102,86,80,111,128,108,104,140,161,138,131,174

%N Expansion of Product_{k>=1} ((1-x^(3*k)) * (1-x^(12*k)) / ((1-x^(6*k-5)) * (1-x^(6*k-1)) * (1-x^(4*k)))).

%H Vaclav Kotesovec, <a href="/A280860/b280860.txt">Table of n, a(n) for n = 0..5000</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 [equation (2.6)].

%F a(n) ~ exp(sqrt(n)*Pi/3) / (3*sqrt(2*n)).

%t nmax = 100; CoefficientList[Series[Product[(1-x^(3*k)) * (1-x^(12*k)) / ((1-x^(6*k-5)) * (1-x^(6*k-1)) * (1-x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x]

%K nonn

%O 0,6

%A _Vaclav Kotesovec_, Jan 09 2017