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

Offset

0,3

References

G. Labelle, Counting enriched multigraphs..., Discrete Math., 217 (2000), 237-248.

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. 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