OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..420
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A001156(k) * k!.
a(n) ~ n! * exp(3 * 2^(-5/3) * Zeta(3/2)^(2/3) * (Pi*n/log(2))^(1/3)) * Zeta(3/2)^(2/3) / (2^(13/6) * sqrt(3) * Pi^(7/6) * n^(7/6) * (log(2))^(n - 1/6)).
MAPLE
a:=series(mul(1/(1-(exp(x)-1)^(k^2)), k=1..100), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - (Exp[x] - 1)^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 20 2018
STATUS
approved