A129620 Square array read by falling antidiagonals: T(n,k) is the number of connected directed multigraphs with loops with n arcs and at most k vertices.

1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 5, 1, 0, 1, 2, 8, 9, 1, 0, 1, 2, 8, 24, 17, 1, 0, 1, 2, 8, 32, 74, 26, 1, 0, 1, 2, 8, 32, 140, 189, 41, 1, 0, 1, 2, 8, 32, 167, 542, 460, 57, 1, 0, 1, 2, 8, 32, 167, 837, 1964, 989, 81, 1, 0, 1, 2, 8, 32, 167, 928, 4167, 6291, 2021, 106, 1, 0

Offset: 0

Author

Benoit Jubin, May 06 2008

Keywords

• nonn
• tabl

Comments

Partial sums of the rows of A139621, i.e., T(n,k) = sum(A139621(n,p),p=0..k).

Examples

			1  1  1  1  1  1  ...
0  1  2  2  2  2  ...
0  1  5  8  8  8  ...
0  1  9 24 32 32  ...
0  1  17  (...)
(...)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1325

Crossrefs

Cf. A138107, A139621.

Formula

T(n,2) = A138107(n,2) - floor(n/2).

If k >= n+1, T(n,k) = A137975(n).

Extensions

Name edited by M. F. Hasler, Jul 31 2017

Terms a(32) and beyond from Andrew Howroyd, Oct 22 2019