OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..385
FORMULA
For n > 0, a(n) = n! + Sum_{k=1..n} binomial(n,k) * k^k * (n-k)!.
a(n) ~ n^n / (1-exp(-1)).
a(n) = n*a(n-1) + n^n, a(0) = 1. - Alois P. Heinz, May 12 2021
MAPLE
a:= proc(n) a(n):= n*a(n-1) + n^n end: a(0):= 1:
seq(a(n), n=0..23); # Alois P. Heinz, May 12 2021
MATHEMATICA
CoefficientList[Series[1/(1+LambertW[-x])/(1-x), {x, 0, 20}], x] * Range[0, 20]!
Flatten[{1, Table[n! + Sum[Binomial[n, k]*k^k*(n-k)!, {k, 1, n}], {n, 1, 20}]}]
PROG
(PARI) x='x+O('x^50); Vec(serlaplace(1/((1 + lambertw(-x))*(1-x)))) \\ G. C. Greubel, Nov 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 18 2016
STATUS
approved