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 A048144 Sum_{k=0..n} (k!)^2*Stirling_2(n,k)^2. 5
 1, 1, 5, 73, 2069, 95401, 6487445, 610093513, 75796724309, 12020754177001, 2369364111428885, 568128719132038153, 162835627057766030549, 54975855375379966645801, 21593185551426744571090325, 9762238510837560633366673993, 5033241437347149354018370856789 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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, Sep 06 2006 Chromatic invariant of the complete bipartite graph K_{n+1,n+1} - Eric W. Weisstein, Jul 11 2011 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 Eric Weisstein's World of Mathematics, Chromatic Invariant Eric Weisstein's World of Mathematics, Complete Bipartite Graph FORMULA 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, Mar 25 2006 CROSSREFS Cf. A212084. Sequence in context: A197764 A126748 A217567 * A144682 A096987 A096538 Adjacent sequences:  A048141 A048142 A048143 * A048145 A048146 A048147 KEYWORD nonn,easy,changed AUTHOR STATUS approved

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