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 A098622 Consider the family of directed multigraphs enriched by the species of set partitions. Sequence gives number of those multigraphs with n labeled loops and arcs. 13
 1, 2, 17, 250, 5465, 162677, 6241059, 297132409, 17075153860, 1159545515804, 91501467848088, 8276847825732141, 848577193578286942, 97672164219292005480, 12518933902769241287267, 1774279753092963892540493, 276351502436571180980604240, 47046745370508674770872396843 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 G. Labelle, Counting enriched multigraphs according to the number of their edges (or arcs), Discrete Math., 217 (2000), 237-248. G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission] FORMULA E.g.f.: exp(-1)*Sum_{n >=0} exp(n^2*(exp(x)-1))/n!. - Vladeta Jovovic, Aug 24 2006 a(n) = Sum_{k=0..n} Stirling2(n,k)*Bell(2*k). - Vladeta Jovovic, Aug 24 2006 E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000110. - Andrew Howroyd, Jan 12 2021 PROG (PARI) \\ here R(n) is A000110 as e.g.f. egfA014507(n)={my(bell=serlaplace(exp(exp(x + O(x^(2*n+1)))-1))); sum(i=0, n, sum(k=0, i, stirling(i, k, 1)*polcoef(bell, 2*k))*x^i/i!) + O(x*x^n)} EnrichedGdlSeq(R)={my(n=serprec(R, x)-1); Vec(serlaplace(subst(egfA014507(n), x, R-polcoef(R, 0))))} R(n)={exp(exp(x + O(x*x^n))-1)} EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021 CROSSREFS Cf. A000110, A014507, A098620, A098621, A098623. Sequence in context: A099694 A099698 A218681 * A020561 A099702 A253549 Adjacent sequences:  A098619 A098620 A098621 * A098623 A098624 A098625 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 26 2004 EXTENSIONS More terms from Vladeta Jovovic, Aug 24 2006 Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007 Terms a(16) and beyond from Andrew Howroyd, Jan 12 2021 STATUS approved

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Last modified May 15 17:50 EDT 2021. Contains 343920 sequences. (Running on oeis4.)