A099712 Consider the family of multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled edges.
1, 1, 4, 30, 338, 5169, 101251, 2446806, 71043973, 2429762734, 96364601877, 4375603494478, 225044659552381, 12990629618136191, 834981228656630494, 59346659738963806022, 4635924974380060251228, 395864230878802130389079, 36773114396103232927777067
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 A000169 as e.g.f.; EnrichedGnSeq defined in A098620. R(n)={-lambertw(-x + O(x*x^n))} EnrichedGnSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021
Formula
E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014500 and R(x) is the e.g.f. of A000169. - Andrew Howroyd, Jan 12 2021
Extensions
Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021