A099699 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled arcs.

1, 1, 8, 108, 2200, 61708, 2249268, 102377404, 5651999688, 370171228504, 28262385542832, 2480108374814480, 247231765611893504, 27722619251007202720, 3467475213036160205984, 480277499859342401636704, 73202023124111697153718080, 12209186681659842887207280448

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..100

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 A000085. - Andrew Howroyd, Jan 12 2021

Prog

(PARI) \\ R(n) is A000085 as e.g.f.; EnrichedGdSeq defined in A098623.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGdSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

Crossrefs

Cf. A000085, A014505, A098623, A099696, A099697, A099698.

Sequence in context: A265277 A336828 A184267 * A084915 A138456 A267660

Adjacent sequences: A099696 A099697 A099698 * A099700 A099701 A099702

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2004

Extensions

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

Status

approved