A099716 Consider the family of multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled edges.

1, 1, 3, 18, 170, 2244, 38686, 834594, 21874433, 681399298, 24797467947, 1039645748808, 49632586028650, 2671404673776080, 160726892084432840, 10729582290405547592, 789572236551678855603, 63682341168165082629698, 5600777517339868668401105

Offset: 0

Author

N. J. A. Sloane, Oct 26 2004

Keywords

• nonn

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]

Crossrefs

Cf. A000272, A014500, A098620, A099717, A099718, A099719.

Programs

PARI

\\ R(n) is A000272 as e.g.f.; EnrichedGnSeq defined in A098620.
R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
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 1 + R(x) is the e.g.f. of A000272. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(12) and beyond from Andrew Howroyd, Jan 12 2021