OFFSET
0,5
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..420
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A033461(k) * k!.
a(n) ~ n! * exp(3 * (Pi/log(2))^(1/3) * ((sqrt(2) - 1) * Zeta(3/2))^(2/3) * n^(1/3) / 4) * ((sqrt(2) - 1) * Zeta(3/2) / Pi)^(1/3) / (2 * sqrt(6) * n^(5/6) * log(2)^(n + 1/6)).
MAPLE
a:=series(mul(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 + (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