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Table read by antidiagonals: T(n,k) is the number of strongly 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).
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%I #2 Mar 31 2012 10:31:22

%S 1,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,2,1,0,1,1,1,1,2,3,

%T 1,0,1,1,1,1,2,3,7,1,0,1,1,1,1,2,3,7,11,1,0,1,1,1,1,2,3,7,11,20,1,0,1,

%U 1,1,1,2,3,7,11,20,29,1,0,1,1,1,1,2,3,7,11,20,30,45,1,0,1,1,1,1,2,3,7,11,20

%N Table read by antidiagonals: T(n,k) is the number of strongly 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).

%C Partial sums of the rows of A139625, i.e., T(n,k) = sum(T139625(n,p),p=0..k).

%C If k>=floor(sqrt(n)), T(n,k) = A139630(n).

%Y Cf. A138352, A136868, A143841.

%K nonn,tabl

%O 0,26

%A _Benoit Jubin_, Sep 02 2008