A099695 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled arcs.

1, 1, 8, 106, 2144, 59844, 2173450, 98648246, 5433864078, 355229741266, 27080154837658, 2373310690810690, 236327564463489838, 26475199136060717618, 3308794737926514931894, 457980967372496137472590, 69761664006643652403884218, 11629282648335699139979015070

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. A014505, A098623, A099692, A099693, A099694.

Programs

PARI

\\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdSeq defined in A098623.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014505. - Andrew Howroyd, Jan 12 2021

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 12 2021