A014505 Number of digraphs with unlabeled (non-isolated) nodes and n labeled edges.

1, 1, 6, 68, 1206, 29982, 981476, 40515568, 2044492988, 123175320988, 8697475219688, 709097832452880, 65934837808883016, 6920436929999656936, 812724019581549433520, 105986960037601701495680

Offset: 0

Author

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

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. A014507.

Formula

E.g.f.: exp(-1) * Sum_{n>=0} (1+x)^(n^2-n) / n!. - Paul D. Hanna, Apr 25 2018

a(n) = n!*exp(-1) * Sum_{k>=sqrt(n)} binomial(k^2-k, n) / k!. - Paul D. Hanna, Apr 25 2018