A362387 Number of directed multigraphs including self-loops on n vertices and n edges.

1, 1, 6, 31, 198, 1270, 8838, 63419, 475796, 3697876, 29793899, 248312750, 2139071800, 19023864211, 174495408060, 1648972635108, 16036927429350, 160338342813918, 1646265278973845, 17340402062779049, 187190960572134321

Offset

0,3

References

F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973, page 88.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = A138107(n,n).

Example

For n=2 we have two edges and two vertices, for a total of six graphs:
* one vertex with two loops attached to it
* one loop attached to each vertex
* two vertices linked by two edges in opposite directions
* two vertices linked by two edges in the same direction
* one vertex with a loop being pointed at
* one vertex with a loop being pointed away from.

Crossrefs

Main diagonal of A138107.

Sequence in context: A097176 A361306 A368535 * A121754 A351818 A200775

Adjacent sequences: A362384 A362385 A362386 * A362388 A362389 A362390

Keyword

nonn

Author

Marko Riedel, Jun 09 2023

Status

approved