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A014501 Number of graphs with loops, having unlabeled (non-isolated) nodes and n labeled edges. 5
1, 2, 7, 43, 403, 5245, 89132, 1898630, 49209846, 1517275859, 54669946851, 2269075206395, 107199678164289, 5707320919486026, 339510756324234931, 22400182888853554291, 1628654713107465602783, 129754625253841669625051 (list; graph; refs; listen; history; text; internal format)
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 A011835

Adjacent sequences:  A014498 A014499 A014500 * A014502 A014503 A014504

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 28 14:27 EST 2020. Contains 338724 sequences. (Running on oeis4.)