A098638 Consider the family of directed multigraphs enriched by the species of odd sets. Sequence gives number of those multigraphs with n labeled loops and arcs.
1, 2, 13, 164, 3127, 82600, 2845775, 122820136, 6446913953, 402413160952, 29343933156485, 2464029760993520, 235446319553848087, 25346231173047308256, 3047931031445529965527, 406412844141860523543392, 59704680455100785101683457, 9608818815170839730520275488
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..200
- G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]
Programs
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PARI
\\ EnrichedGdlSeq defined in A098622. EnrichedGdlSeq(sinh(x + O(x*x^20))) \\ Andrew Howroyd, Jan 12 2021
Formula
E.g.f.: exp(-1)*Sum_{n>=0}(1+sinh(x))^(n^2)/n!. - Vladeta Jovovic, Mar 04 2008
E.g.f.: B(sinh(x)) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021
Extensions
Missing a(10) inserted and terms a(13) and beyond from Andrew Howroyd, Jan 12 2021