A099694 Consider the family of directed multigraphs enriched by the species of directed sets. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 2, 17, 244, 5283, 156092, 5954547, 282221828, 16159327961, 1094056231572, 86116276633357, 7773114989571400, 795480206815177651, 91417037615848058160, 11701283925663217478843, 1656436690705751478232180, 257730676653629520748175377, 43837005194184348815823808500

Offset

0,2

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]

Formula

E.g.f.: B(2*exp(x) - x - 2) where B(x) is the e.g.f. of A014507. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is e.g.f. of 1, 1, 2, 2, 2, ...; EnrichedGdlSeq defined in A098622.
R(n)={2*exp(x + O(x*x^n)) - x - 1}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A014507, A098622, A099692, A099693, A099695.

Sequence in context: A319947 A361194 A342205 * A099698 A218681 A349293

Adjacent sequences: A099691 A099692 A099693 * A099695 A099696 A099697

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved