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

0,3

References

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

Links

Table of n, a(n) for n=0..15.

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]

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

Crossrefs

Cf. A014507.

Sequence in context: A349557 A140606 A355219 * A363396 A274722 A347927

Adjacent sequences: A014502 A014503 A014504 * A014506 A014507 A014508

Keyword

nonn

Author

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

Status

approved