OFFSET
0,2
COMMENTS
In general, for m > 0, if g.f. = Product_{k>=1} (1 + m*x^k)^k then a(n) ~ c^(1/6) * exp(3^(2/3) * c^(1/3) * n^(2/3) / 2) / (3^(2/3) * (m+1)^(1/12) * sqrt(2*Pi) * n^(2/3)), where c = Pi^2*log(m) + log(m)^3 - 6*polylog(3, -1/m).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
FORMULA
a(n) ~ c^(1/6) * exp(3^(2/3) * c^(1/3) * n^(2/3) / 2) / (2^(2/3) * 3^(2/3) * sqrt(Pi) * n^(2/3)), where c = Pi^2*log(3) + log(3)^3 - 6*polylog(3, -1/3) = 14.092743327504459346835224018840792668682349056875722467... .
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+3*x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 04 2016
STATUS
approved