A136868 Table read by antidiagonals: T(n,k) is the number of connected directed multigraphs with loops 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, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 4, 1, 0, 1, 2, 6, 7, 1, 0, 1, 2, 6, 14, 12, 1, 0, 1, 2, 6, 17

Offset: 0

Author

Benoit Jubin, May 11 2008

Keywords

• more
• nonn
• tabl

Comments

Partial sums of the rows of A139624, i.e., T(n,k) = sum(T139624(n,p),p=0..k).

T(0,k) = 1 for k>=0; T(n,0) = 0 and T(n,1) = 1 for n>0.

If k>=n+1, T(n,k) = A139629(n).

Examples

			Triangle begins:
1,
1, 0,
1, 1, 0,
1, 2, 1, 0,
1, 2, 4, 1, 0,
1, 2, 6, 7, 1, 0,
1, 2, 6,14,12, 1, 0,
		

Crossrefs

Cf. A138352.