A099706 Consider the family of directed multigraphs enriched by the species of directed graphs. Sequence gives number of those multigraphs with n labeled loops and arcs.
1, 4, 84, 3568, 305712, 87782720, 144600947392, 1139235294403328, 37012349010095737088, 4840037457225169875031040, 2535930555678883610642223895552, 5317274645187046706095607711946092544, 44602319906972740832371696997145322907873280
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.; EnrichedGdlSeq defined in A098622. R(n)={sum(k=0, n, 2^(k^2)*x^k/k!) + O(x*x^n)} EnrichedGdlSeq(R(15)) \\ 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 A002416. - Andrew Howroyd, Jan 12 2021
Extensions
Terms a(10) and beyond from Andrew Howroyd, Jan 12 2021