A099718 Consider the family of directed multigraphs enriched by the species of trees. Sequence gives number of those multigraphs with n labeled loops and edges.

1, 2, 15, 207, 4274, 120698, 4408714, 200482089, 11035845002, 719691942986, 54661283926338, 4768412660292713, 472309503983879356, 52604316569196875434, 6533611563916740388476, 898472724512273277951811, 135941600045496082012663932, 22505828691354514668620263242

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(R(x)) where B(x) is the e.g.f. of A014507 and 1 + R(x) is the e.g.f. of A000272. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A000272 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={my(w=lambertw(-x + O(x*x^n))); 1 - w - w^2/2}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A000272, A014507, A098622, A099716, A099717, A099719.

Sequence in context: A124558 A020565 A282521 * A143881 A298692 A361617

Adjacent sequences: A099715 A099716 A099717 * A099719 A099720 A099721

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved