A098627 Consider the family of directed multigraphs enriched by the species of derangements. Sequence gives number of those multigraphs with n labeled arcs.

1, 0, 1, 2, 27, 164, 2335, 25458, 437241, 6965112, 145640817, 3057675290, 76814951587, 2003471245164, 59438049704943, 1855131250113498, 63937099992148785, 2327591284996635888, 91854272591000172321, 3828194864278619367474, 170846746588575658999147

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..200
• G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Crossrefs

Cf. A000166, A014505, A098623, A098624, A098625, A098626.

Programs

PARI

\\ R(n) is A000166 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(-x + O(x*x^n))/(1-x)}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Formula

E.g.f.: B(R(x)) where B(x) is the e.g.f. of A014505 and 1 + R(x) is the e.g.f. of A000166. - Andrew Howroyd, Jan 12 2021

Extensions

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