A280947 - OEIS

%I #6 Jan 12 2017 12:36:40

%S 1,2,4,8,14,24,40,64,100,153,230,340,496,714,1016,1432,1998,2764,3793,

%T 5166,6988,9392,12546,16664,22016,28940,37860,49306,63936,82568,

%U 106216,136128,173844,221256,280680,354952,447530,562624,705352,881920,1099840,1368188

%N Expansion of Product_{k>=1} (1 - x^(18*k)) * (1 - x^(18*k-9)) * (1 + x^k) / (1 - x^k).

%H Vaclav Kotesovec, <a href="/A280947/b280947.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 S78.

%F a(n) ~ sqrt(5) * exp(5*Pi*sqrt(n/3)/3) / (4 * 3^(7/4) * n^(3/4)).

%t nmax=50; CoefficientList[Series[Product[(1-x^(18*k))*(1-x^(18*k-9))*(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 11 2017