A098626 Consider the family of directed multigraphs enriched by the species of derangements. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 0, 2, 4, 57, 348, 5235, 57930, 1037540, 16842496, 363889755, 7792175070, 201054289293, 5345844537876, 162234861271288, 5156725529935952, 181284205622239755, 6713109719185427600, 269652617328843102055, 11418447984579685481310, 517839485352765454438270

Offset

0,3

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..200

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 A000166. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A000166 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(-x + O(x*x^n))/(1-x)}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A000166, A014507, A098622, A098624, A098625, A098627.

Sequence in context: A230884 A362735 A185182 * A012370 A012366 A009513

Adjacent sequences: A098623 A098624 A098625 * A098627 A098628 A098629

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 12 2021

Status

approved