OFFSET
0,2
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 7.036711302278424796297167109247361745558645910729132828752853658917..., c = 2.3254811458... .
MATHEMATICA
Table[SeriesCoefficient[Product[(1+x^k)^3/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+3)/2}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r^2 /.FindRoot[-Pi^2/12 - Log[r]^2/3 + 1/2*Log[1+r]^2 + PolyLog[2, 1/(1+r)] == 0, {r, E}, WorkingPrecision->100]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 10 2015
STATUS
approved