A099704 Consider the family of multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled edges.
1, 2, 24, 776, 79840, 35397440, 69619053504, 564929183555840, 18464894708236907776, 2418517115222622481308160, 1267747370909677813160722947072, 2658511777246500251150215101758228480, 22300872810108738542496498718468714032205824
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..50
- 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 A002416 as e.g.f.; EnrichedGnSeq defined in A098620. R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)} EnrichedGnSeq(R(15)) \\ Andrew Howroyd, Jan 12 2021
Formula
E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 and 1 + R(x) is the e.g.f. of A002416. - Andrew Howroyd, Jan 12 2021
Extensions
Terms a(10) and beyond from Andrew Howroyd, Jan 12 2021