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A122419 Number of labeled digraphs with n arcs and with no vertex of indegree 0. 4
1, 0, 1, 8, 93, 1354, 23900, 496244, 11855700, 320428318, 9667220397, 322072882348, 11744421711587, 465270864839688, 19899234175413257, 913836170567749048, 44849438199960187278, 2342666125012348876152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A122418(k). G.f.: Sum(((1+x)^(n-1)-1)^n,n=0..infinity).

a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.08904589343883135100956914504938... . - Vaclav Kotesovec, May 07 2014

MAPLE

A122418 := proc(n) option remember ; add( combinat[stirling2](n, k)*(k-1)^n*k!, k=0..n) ; end: A122419 := proc(n) option remember ; add( combinat[stirling1](n, k)*A122418(k), k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, ", A122419(n)) ; od ; # R. J. Mathar, May 18 2007

MATHEMATICA

nmax=20; CoefficientList[Series[Sum[((1+x)^(n-1)-1)^n, {n, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, May 06 2014 *)

CROSSREFS

Cf. A122420, A122400.

Sequence in context: A099291 A087579 A194043 * A319176 A299034 A299339

Adjacent sequences:  A122416 A122417 A122418 * A122420 A122421 A122422

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Sep 03 2006

EXTENSIONS

More terms from R. J. Mathar, May 18 2007

STATUS

approved

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Last modified April 10 10:39 EDT 2021. Contains 342845 sequences. (Running on oeis4.)