A099714 Consider the family of directed multigraphs enriched by the species of arborescences. Sequence gives number of those multigraphs with n labeled loops and arcs.
1, 2, 17, 258, 5771, 174528, 6770119, 324895980, 18781627193, 1281239711000, 101465766593553, 9204346831406488, 945843113150930899, 109072242262950463552, 14001689466624210245831, 1986950788160317182000976, 309800790825415866952825137, 52786928631190620809803203872
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
-
PARI
\\ R(n) is A000169 as e.g.f.; EnrichedGdlSeq defined in A098622. R(n)={-lambertw(-x + O(x*x^n))} 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 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