A098630 Consider the family of directed multigraphs enriched by the species of parts. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 4, 60, 1624, 66240, 3711200, 269670208, 24435113216, 2682916389632, 349223324753408, 52965538033020928, 9229753832340117504, 1826647528631522463744, 406579171521484851396608, 100934277604965329345822720, 27746271707522968205726416896

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. A000079, A014507, A098622, A098628, A098629, A098631.

Programs

PARI

a(n) = {2^n*sum(k=0, 2*n, stirling(2*n,k,2))} \\ Andrew Howroyd, Jan 12 2021

PARI

\\ R(n) is A000079 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(2*x + O(x*x^n))}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

a(n) = 2^n*Bell(2*n). - Vladeta Jovovic, Aug 22 2006

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 A000079. - Andrew Howroyd, Jan 12 2021

Extensions

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