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A122420 Number of labeled directed multigraphs with n arcs and with no vertex of indegree 0. 4
1, 0, 1, 10, 120, 1778, 31685, 661940, 15882128, 430607370, 13022755068, 434697574538, 15875944361864, 629756003982336, 26963278837704185, 1239382820431888898, 60875147436141987437, 3181961834442383306068 (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.: A(x/(1-x)) where A(x) is g.f. for A122419.

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 = 0.1221803955695846906452721220983425... . - Vaclav Kotesovec, May 07 2014

MAPLE

A122418 := proc(n) option remember ; add( combinat[stirling2](n, k)*(k-1)^n*k!, k=0..n) ; end: A122420 := proc(n) option remember ; add( abs(combinat[stirling1](n, k))*A122418(k), k=0..n)/n! ; end: for n from 0 to 30 do printf("%d, ", A122420(n)) ; od ; # R. J. Mathar, May 18 2007

MATHEMATICA

Table[1/n!*Sum[Abs[StirlingS1[n, k]]*Sum[(m-1)^k*m!*StirlingS2[k, m], {m, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 07 2014 *)

CROSSREFS

Cf. A104209.

Sequence in context: A320760 A034255 A051582 * A069671 A138445 A138496

Adjacent sequences:  A122417 A122418 A122419 * A122421 A122422 A122423

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 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)