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A122420
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Number of labeled directed multigraphs with n arcs and with no vertex of indegree 0.
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3
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1, 0, 1, 10, 120, 1778, 31685, 661940, 15882128, 430607370, 13022755068, 434697574538, 15875944361864, 629756003982336, 26963278837704185, 1239382820431888898, 60875147436141987437, 3181961834442383306068
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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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.
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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 (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
| Cf. A104209.
Sequence in context: A027568 A034255 A051582 * A069671 A138445 A138496
Adjacent sequences: A122417 A122418 A122419 * A122421 A122422 A122423
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 03 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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