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 A099718 Consider the family of directed multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled loops and edges. 2
 1, 2, 15, 207, 4274, 120698, 4408714, 200482089, 11035845002, 719691942986, 54661283926338, 4768412660292713, 472309503983879356, 52604316569196875434, 6533611563916740388476, 898472724512273277951811, 135941600045496082012663932, 22505828691354514668620263242 (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..100 G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission] FORMULA 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 A000272. - Andrew Howroyd, Jan 12 2021 PROG (PARI) \\ R(n) is A000272 as e.g.f.; EnrichedGdlSeq defined in A098622. R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2} EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021 CROSSREFS Cf. A000272, A014507, A098622, A099716, A099717, A099719. Sequence in context: A124558 A020565 A282521 * A143881 A298692 A132493 Adjacent sequences:  A099715 A099716 A099717 * A099719 A099720 A099721 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 26 2004 EXTENSIONS Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021 STATUS approved

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Last modified January 16 14:39 EST 2022. Contains 350376 sequences. (Running on oeis4.)