OFFSET
0,3
FORMULA
a(n) = Sum_{k=1..n} k! * k^n * binomial(n-1,k-1) for n > 0.
a(n) ~ exp(exp(-1)) * n! * n^n. - Vaclav Kotesovec, Feb 18 2023
MATHEMATICA
nmax = 20; CoefficientList[1 + Series[Sum[k! * (k * x/(1 - k*x))^k, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 18 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, k!*(k*x/(1-k*x))^k))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, k!*k^n*binomial(n-1, k-1)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 29 2022
STATUS
approved