A139623 Table read by rows: T(n,k) is the number of directed multigraphs with loops and no vertex of degree 0, with n arcs and k vertices, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).

1, 1, 1, 4, 3, 1, 1, 7, 12, 9, 3, 1, 1, 13

Offset: 1

Author

Benoit Jubin, May 01 2008

Keywords

• nonn
• tabf
• more

Comments

Length of the n^th row: 2n.

T(n,1) = T(n,2n) = 1 and T(n,2n-1) = 3 if n>1.

Row sums: A139628.

Examples

			Triangle begins
1, 1;
1, 4, 3, 1;
1, 7, 12, 9, 3, 1;
		

Crossrefs

Cf. A136564, A139624, A139625.