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A086331 E.g.f.: exp(x)/(1+LambertW(-x)). 28
1, 2, 7, 43, 393, 4721, 69853, 1225757, 24866481, 572410513, 14738647221, 419682895325, 13094075689225, 444198818128313, 16278315877572141, 640854237634448101, 26973655480577228769, 1208724395795734172705 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A000312 [Tilman Neumann, Dec 13 2008]

a(n) is the number of partial functions on {1,2,...,n} that are endofunctions.  See comments in A000169 and A126285 by Frank T. Adams-Waters. - Geoffrey Critzer, Dec 19 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

V. Kotesovec, Interesting asymptotic formulas for binomial sums, Jun 09 2013

FORMULA

a(n) = 1 + Sum_{k=1..n} binomial(n, k)*k^k. [Clarified by J. M. Bergot, Jul 11 2016

a(n) ~ e^(1/e)*n^n * (1 + 1/(2*e*n)) ~ 1.444667861... * n^n. - Vaclav Kotesovec, Nov 27 2012

EXAMPLE

a(2)= 7 because {}->{},1->1,2->2, and the four functions from {1,2} into {1,2}. Note A000169(2)=9 because it counts these 7 and 1->2,2->1.

MATHEMATICA

nn=10; t=Sum[n^(n-1)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[Series[Exp[x]/(1-t), {x, 0, nn}], x]  (* Geoffrey Critzer, Dec 19 2011 *)

PROG

(PARI) a(n) = sum(k=0, n, binomial(n, k)*k^k ); \\ Joerg Arndt, May 10 2013

CROSSREFS

Cf. A069856, A277454, A277456.

Sequence in context: A078676 A265229 A286684 * A121418 A014501 A197910

Adjacent sequences:  A086328 A086329 A086330 * A086332 A086333 A086334

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Sep 01 2003

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)