OFFSET
0,5
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} (1 + x^(m*k-1))^(m*k-1), then a(n, m) ~ exp(2^(-4/3) * 3^(4/3) * m^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(1/6 + 1/(2*m) + m/12) * 3^(1/3) * m^(1/6) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 17 2017
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(2^(-4/3) * 3^(4/3) * 5^(-1/3) * Zeta(3)^(1/3) * n^(2/3)) * Zeta(3)^(1/6) / (2^(41/60) * 3^(1/3) * 5^(1/6) * sqrt(Pi) * n^(2/3)). - Vaclav Kotesovec, Apr 17 2017
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^(5*k-1))^(5*k-1), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 17 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 17 2017
STATUS
approved