%I #7 Oct 01 2015 01:42:16

%S 1,6,18,44,102,216,428,816,1494,2650,4584,7740,12804,20808,33264,

%T 52400,81462,125100,189966,285516,425016,627040,917436,1331856,

%U 1919332,2746926,3905784,5519352,7754064,10833192,15055216,20817600,28647414,39241336,53517060

%N Expansion of Product_{k>=0} ((1+x^(2*k+1))/(1-x^(2*k+1)))^3.

%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 11.

%F a(n) ~ exp(Pi*sqrt(3*n/2)) * 3^(1/4) / (8 * 2^(1/4) * n^(3/4)).

%t nmax=60; CoefficientList[Series[Product[((1+x^(2*k+1))/(1-x^(2*k+1)))^3,{k,0,nmax}],{x,0,nmax}],x]

%Y Cf. A015128, A156616.

%Y Cf. A080054, A007096, A014969, A261648, A014970, A014972, A103261.

%Y Cf. A261610, A261649, A261651.

%Y Cf. A261611, A261650, A261652.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Aug 28 2015