A099698 Consider the family of directed multigraphs enriched by the species of involutions. Sequence gives number of those multigraphs with n labeled loops and arcs.

1, 2, 17, 248, 5403, 160420, 6142567, 291996934, 16759322733, 1136940595762, 89641455771637, 8102778995663368, 830222723124364047, 95509354134959796556, 12236166882713532940611, 1733521075683722202738222, 269910543278748394820341769, 45936441912756036235229989058

Offset: 0

Author

N. J. A. Sloane, Jun 25 2017

Keywords

• nonn

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]

Crossrefs

Cf. A000085, A014507, A098622, A099696, A099697, A099699.

Programs

PARI

\\ R(n) is A000085 as e.g.f.; EnrichedGdlSeq defined in A098622.
R(n)={exp(x+x^2/2 + O(x*x^n))}
EnrichedGdlSeq(R(20)) \\ Andrew Howroyd, Jan 12 2021

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 A000085. - Andrew Howroyd, Jan 12 2021

Extensions

Dead sequence restored, corrected and extended by Andrew Howroyd, Jan 12 2021