A014501 Number of graphs with loops, having unlabeled (non-isolated) nodes and n labeled edges.

1, 2, 7, 43, 403, 5245, 89132, 1898630, 49209846, 1517275859, 54669946851, 2269075206395, 107199678164289, 5707320919486026, 339510756324234931, 22400182888853554291, 1628654713107465602783, 129754625253841669625051

Offset

0,2

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..200

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+x/2)*Sum((1+x)^binomial(n+1, 2)/n!, n=0..infinity) [probably in the Labelle paper]. - Vladeta Jovovic, Apr 27 2004

Crossrefs

Row n=2 of A331161.

Cf. A020554, A020555, A014500.

Sequence in context: A286684 A086331 A121418 * A197910 A228230 A340335

Adjacent sequences: A014498 A014499 A014500 * A014502 A014503 A014504

Keyword

nonn

Author

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

Status

approved