OFFSET
0,2
COMMENTS
In general, for m>=3, coefficient of x^n in Product_{k>=1} ((1+x^k)/(1-x^k))^(n^m) is asymptotic to 2^n * n^(m*n) / n!.
FORMULA
a(n) ~ 2^(n - 1/2) * exp(n) * n^(2*n - 1/2) / sqrt(Pi).
MATHEMATICA
nmax = 20; Table[SeriesCoefficient[Product[((1+x^k)/(1-x^k))^(n^3), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
nmax = 20; Table[SeriesCoefficient[(QPochhammer[-1, x]/2/QPochhammer[x])^(n^3), {x, 0, n}], {n, 0, nmax}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, May 13 2018
STATUS
approved