OFFSET
0,3
COMMENTS
The number of functions from {1,2,...,n} into a subset of {1,2,...,n} summed over all subsets. - Geoffrey Critzer, Sep 16 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
V. Kotesovec, Interesting asymptotic formulas for binomial sums, Jun 09 2013
FORMULA
E.g.f.: 1/(1+LambertW(-x*exp(x))). - Vladeta Jovovic, Mar 29 2008
a(n) ~ (n/(e*LambertW(1/e)))^n/sqrt(1+LambertW(1/e)). - Vaclav Kotesovec, Nov 26 2012
O.g.f.: Sum_{n>=0} n^n * x^n / (1 - n*x)^(n+1). - Paul D. Hanna, May 22 2018
MAPLE
seq(add(binomial(n, k)*k^n, k=0..n), n=0..17); # Peter Luschny, Jun 09 2015
MATHEMATICA
Table[Sum[Binomial[n, k]k^n, {k, 0, n}], {n, 1, 20}] (* Geoffrey Critzer, Sep 16 2012 *)
PROG
(PARI) x='x+O('x^50); Vec(serlaplace(1/(1 + lambertw(-x*exp(x))))) \\ G. C. Greubel, Nov 10 2017
(PARI) a(n) = sum(k=0, n, binomial(n, k)*k^n); \\ Michel Marcus, Nov 10 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Jun 07 2002
EXTENSIONS
Offset set to 0 and a(0) = 1 prepended by Peter Luschny, Jun 09 2015
E.g.f. edited to include a(0)=1 by Robert Israel, Jun 09 2015
STATUS
approved