OFFSET
0,8
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
FORMULA
G.f.: exp(Sum_{k>=1} x^(4*k)/(k*(1-x^(3*k))^2).
a(n) ~ c * Zeta(3)^(19/108) * exp(-Pi^4/(3888*Zeta(3)) - Pi^2 * n^(1/3) / (2^(4/3) * 3^(7/3) * Zeta(3)^(1/3)) + 3^(1/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(2/3)) / (2^(35/108) * 3^(23/27) * sqrt(Pi) * n^(73/108)), where c = 3^(1/6) * sqrt(2*Pi) * exp(A263031) / Gamma(1/3) = 1.107474840397395849254161220076423560365022...
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
`if`(irem(d-1, 3)=0, (d-1)/3, 0),
d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..60); # after Alois P. Heinz, Oct 17 2015
MATHEMATICA
nmax = 60; CoefficientList[Series[Product[1/(1-x^(3*k+1))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 60; CoefficientList[Series[E^Sum[x^(4*k)/(k*(1-x^(3*k))^2), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 17 2015
STATUS
approved