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Search: id:A122419
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| A122419 |
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Number of labeled digraphs with n arcs and with no vertex of indegree 0. |
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+0
3
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| 1, 0, 1, 8, 93, 1354, 23900, 496244, 11855700, 320428318, 9667220397, 322072882348, 11744421711587, 465270864839688, 19899234175413257, 913836170567749048, 44849438199960187278, 2342666125012348876152
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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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).
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), May 18 2007
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CROSSREFS
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Cf. A122420, A122400.
Sequence in context: A137159 A099291 A087579 this_sequence A121161 A098269 A010565
Adjacent sequences: A122416 A122417 A122418 this_sequence A122420 A122421 A122422
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KEYWORD
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easy,nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 03 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2007
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