OFFSET
0,3
FORMULA
a(n) = n! * Sum_{i=0..n} Sum_{j=0..n-i} i^j * Stirling2(n-i-j,j)/(n-i-j)!.
a(n) ~ n! / ((1 - r + exp(r)*r*(1 + r)) * r^n), where r = 0.60489399462026660841486230237937164068755854932856922096976397761... is the root of the equation exp(r*(exp(r)-1)) = 1/r. - Vaclav Kotesovec, Apr 13 2023
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x*(exp(x)-1)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 12 2023
STATUS
approved