OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..232
FORMULA
a(n) = exp(1/n) * n^n * Gamma(n+1, 1/n).
a(n) ~ n^n * n!.
a(n) = n! * [x^n] exp(x)/(1 - n*x). - Ilya Gutkovskiy, Sep 18 2018
a(n) = floor(n^n*n!*exp(1/n)), n > 0. - Peter McNair, Dec 20 2021
MAPLE
a := n -> simplify(hypergeom([1, -n], [], -n)):
seq(a(n), n=0..15); # Peter Luschny, Oct 03 2018
# second Maple program:
b:= proc(n, k) option remember;
1 + `if`(n>0, k*n*b(n-1, k), 0)
end:
a:= n-> b(n$2):
seq(a(n), n=0..17); # Alois P. Heinz, May 09 2020
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*n^k*k!, {k, 0, n}], {n, 1, 20}]}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k) * n^k * k!); \\ Michel Marcus, Sep 18 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 16 2016
STATUS
approved