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Search: id:A048144
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| A048144 |
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Sum_{k=0..n} (k!)^2*Stirling_2(n,k)^2. |
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+0
4
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| 1, 1, 5, 73, 2069, 95401, 6487445, 610093513, 75796724309, 12020754177001, 2369364111428885, 568128719132038153, 162835627057766030549, 54975855375379966645801, 21593185551426744571090325, 9762238510837560633366673993, 5033241437347149354018370856789
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of digraphs with loops, with labeled vertices and labeled arcs, with n arcs, and with no vertex of indegree 0 or outdegree 0, cf. A121936, A122418, A122399. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 06 2006
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FORMULA
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E.g.f.: Sum_{n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*(exp(j*x)-1)^n. a(n) = Sum_{k=0..n} Stirling2(n,k)*k!*A104602(k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 25 2006
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CROSSREFS
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Sequence in context: A005259 A062440 A126748 this_sequence A096987 A096538 A012640
Adjacent sequences: A048141 A048142 A048143 this_sequence A048145 A048146 A048147
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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