A020560 Number of ordered oriented multigraphs on n labeled arcs (without loops).

1, 1, 8, 110, 2262, 63822, 2335856, 106643980, 5901564892, 387251339836, 29612207398688, 2601877956513640, 259646660158526856, 29140784853464966632, 3647614440065070983488, 505553321559685235600720, 77096697572750991426551056, 12864789849511242132008021520

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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

a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n, k) * A020556(k). - Sean A. Irvine, Apr 24 2019

Crossrefs

Cf. A020556.

Sequence in context: A098623 A297971 A076151 * A144813 A079660 A131621

Adjacent sequences: A020557 A020558 A020559 * A020561 A020562 A020563

Keyword

nonn

Author

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

Status

approved