OFFSET
0,3
FORMULA
a(n) = n! * [x^n] 1/(1 - n*x*exp(x)).
From Vaclav Kotesovec, Feb 19 2022: (Start)
a(n) ~ exp(1) * n! * n^n.
a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n-1). (End)
MATHEMATICA
Join[{1}, Table[n!*Sum[n^(n - k)*(n - k)^k/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Feb 19 2022 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, n^(n-k)*(n-k)^k/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 18 2022
STATUS
approved