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A072034 a(n) = Sum_{k=0..n} binomial(n,k)*k^n. 12
1, 1, 6, 54, 680, 11000, 217392, 5076400, 136761984, 4175432064, 142469423360, 5372711277824, 221903307604992, 9961821300640768, 482982946946734080, 25150966159083264000, 1400031335107317628928, 82960293298087664648192 (list; graph; refs; listen; history; text; internal format)
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

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 *)

CROSSREFS

Cf. A088789, A242446, A256016.

Sequence in context: A034001 A084062 A137591 * A167571 A138434 A217238

Adjacent sequences:  A072031 A072032 A072033 * A072035 A072036 A072037

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

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Last modified December 10 11:39 EST 2016. Contains 279001 sequences.