A020559 Number of ordered multigraphs on n labeled edges (with loops).

1, 2, 11, 97, 1219, 20385, 433022, 11296844, 352866598, 12938878499, 548257129281, 26503637228615, 1446212232918009, 88278080019931590, 5981590442549971867, 446907535344317788261, 36602523445840041088223

Offset: 0

Author

Gilbert Labelle (gilbert(AT)lacim.uqam.ca), Simon Plouffe

Keywords

• nonn

References

• G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004.

Links

• G. Labelle, Counting enriched multigraphs according to the number of their edges (or arcs), Discrete Math., 217 (2000), 237-248.
• G. Paquin, Dénombrement de multigraphes enrichis, Mémoire, Math. Dept., Univ. Québec à Montréal, 2004. [Cached copy, with permission]

Crossrefs

Cf. A020555, A020558.

Formula

E.g.f.: exp((3*x-2)/(2-2*x))*Sum_{n>=0}1/(n!*(1-x)^binomial(n+1, 2)). - Vladeta Jovovic, May 02 2004

a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n, k) * A020555(k). - Sean A. Irvine, Apr 24 2019