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%I #6 Jan 14 2022 19:45:35
%S 1,1,0,1,1,0,1,1,1,0,1,1,2,1,0,1,1,2,3,1,0,1,1,2,4,7,1,0,1,1,2,4,11,
%T 11,1,0,1,1,2,4,12,30,20,1,0,1,1,2,4,12,36,93,29,1,0,1,1,2,4,12,37,
%U 152,237,45,1,0,1,1,2,4,12,37,161,587,579,61,1,0
%N Table read by antidiagonals: T(n,k) is the number of strongly connected directed multigraphs with loops with n arcs and up to k vertices.
%H Andrew Howroyd, <a href="/A143841/b143841.txt">Table of n, a(n) for n = 0..860</a>
%F T(n,k) = Sum_{p=0..k} A139622(n,p).
%F T(n,k) = A139627(n) for k >= n.
%F T(n,2) = A129620(n,2) - n*(n-1)/2.
%e Array begins:
%e =============================================
%e n\k | 0 1 2 3 4 5 6 7 8
%e ----+----------------------------------------
%e 0 | 1 1 1 1 1 1 1 1 1 ...
%e 1 | 0 1 1 1 1 1 1 1 1 ...
%e 2 | 0 1 2 2 2 2 2 2 2 ...
%e 3 | 0 1 3 4 4 4 4 4 4 ...
%e 4 | 0 1 7 11 12 12 12 12 12 ...
%e 5 | 0 1 11 30 36 37 37 37 37 ...
%e 6 | 0 1 20 93 152 161 162 162 162 ...
%e 7 | 0 1 29 237 587 725 737 738 738 ...
%e 8 | 0 1 45 579 2249 3610 3911 3927 3928 ...
%e ...
%o (PARI) \\ See PARI link in A350489 for program code.
%o A(n)={my(T=A139622rows(n)), M=matrix(n+1, n+1, i, j, if(i==1, 1, sum(k=1, min(i-1,j-1), data[i-1][k])))); M}
%o { my(M=A(8)); for(n=1, #M~, print(M[n,])) } \\ _Andrew Howroyd_, Jan 14 2022
%Y Partial sums of the rows of A139622.
%Y Main diagonal is A139627.
%Y Cf. A138107, A129620, A143842, A350489.
%K nonn,tabl
%O 0,13
%A _Benoit Jubin_, Sep 02 2008
%E Name clarified and terms a(32) and beyond from _Andrew Howroyd_, Jan 14 2022
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