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

0,4

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 A014505 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.; EnrichedGdSeq defined in A098623.
R(n)={exp(-x + O(x*x^n))/(1-x)}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

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

Sequence in context: A041801 A166942 A119351 * A263930 A051766 A058406

Adjacent sequences: A098624 A098625 A098626 * A098628 A098629 A098630

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved