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

0,2

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

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

Prog

(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

Crossrefs

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

Sequence in context: A013484 A013485 A324959 * A336637 A330069 A211309

Adjacent sequences: A098627 A098628 A098629 * A098631 A098632 A098633

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved