A020558 - OEIS

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A020558

Number of ordered multigraphs on n labeled edges (without loops).

1, 1, 4, 27, 274, 3874, 71995, 1682448, 47840813, 1615315141, 63566760077, 2873099980637, 147384910116793, 8496500896980637, 545845612016485842, 38797966029876716897, 3032005571734589578076

(list; graph; refs; listen; history; text; internal format)

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..16.

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((3*x-2)/(2-2*x))*Sum(1/(n!*(1-x)^binomial(n, 2)), n = 0 .. infinity). a(n) = Sum((-1)^(n-k)*Stirling1(n, k)*A020554(k), k=0..n). - Vladeta Jovovic, May 02 2004

E.g.f.: exp(x/(2-2*x))*Sum(A020556(n)*(-log(1-x)/2)^n/n!, n=0..infinity). - Vladeta Jovovic, May 02 2004

CROSSREFS

Sequence in context: A052871 A104653 A194787 * A259485 A362699 A193467

Adjacent sequences: A020555 A020556 A020557 * A020559 A020560 A020561

KEYWORD

nonn

AUTHOR

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

STATUS

approved