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.
1, 2, 15, 207, 4274, 120698, 4408714, 200482089, 11035845002, 719691942986, 54661283926338, 4768412660292713, 472309503983879356, 52604316569196875434, 6533611563916740388476, 898472724512273277951811, 135941600045496082012663932, 22505828691354514668620263242
Offset: 0
Keywords
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]
Programs
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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
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
Extensions
Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021