A099702 Consider the family of directed multigraphs enriched by the species of simple graphs. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 2, 17, 256, 5719, 173446, 6768075, 328288840, 19468007553, 1458080017522, 183476204746761, 87209577493989776, 154656821805639801687, 617619828457724835488214, 5008102331929281541386123923, 81618549234469098721106601012472, 2666950050438611111026601803629686849

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..50

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 A006125. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A006125 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A006125, A014507, A098622, A099700, A099701, A099703.

Sequence in context: A349293 A098622 A020561 * A253549 A002590 A029735

Adjacent sequences: A099699 A099700 A099701 * A099703 A099704 A099705

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved