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A139622 Triangle read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices.

%I A139622 #24 Jan 14 2022 19:45:20
%S A139622 1,1,1,1,2,1,1,6,4,1,1,10,19,6,1,1,19,73,59,9,1,1,28,208,350,138,12,1,
%T A139622 1,44,534,1670,1361,301,16,1,1,60,1215,6476,9724,4364,575,20,1,1,85,
%U A139622 2542,21898,55707,45284,12131,1042,25,1,1,110,4951,65789,268329,365063,175416,30090,1749,30,1
%N A139622 Triangle read by rows: T(n,k) is the number of strongly connected directed multigraphs with loops, with n arcs and k vertices.
%H A139622 Andrew Howroyd, <a href="/A139622/b139622.txt">Table of n, a(n) for n = 1..820</a> (rows 1..40)
%H A139622 R. J. Mathar, <a href="http://arxiv.org/abs/1709.09000">Statistics on Small Graphs</a>, arXiv:1709.09000 (2017) Table 73.
%F A139622 T(n,1) = T(n,n) = 1.
%F A139622 T(n,2) = A139621(n,2) - n(n+1)/2.
%e A139622 Triangle begins:
%e A139622     1
%e A139622     1    1
%e A139622     1    2    1
%e A139622     1    6    4    1
%e A139622     1   10   19    6    1
%e A139622     1   19   73   59    9    1
%e A139622     1   28  208  350  138   12    1
%e A139622     1   44  534 1670 1361  301   16  1
%e A139622     ...
%e A139622 T(4 edges, 2 vertices)=6: one graph 1->1, 1->1, 2->1, 1->2; one graph 1->1, 2->1, 2->1, 1->2; one graph 1->1, 1->2, 1->2, 2->1; one graph 1->1, 1->2, 2->1, 2->2; one graph 2->1, 2->1, 2->1, 1->2; one graph 1->2, 1->2, 2->1, 2->1.
%e A139622 T(4 edges, 3 vertices)=4: one graph 1->1, 2->1, 3->2, 1->3; one graph 2->1, 2->1, 3->2, 1->3; one graph 2->1, 3->1, 1->2, 1->3; one graph 2->1, 3->1, 1->2, 2->3.
%o A139622 (PARI) \\ See PARI link in A350489 for program code.
%o A139622 { my(A=A139622rows(10)); for(n=1, #A, print(A[n])) } \\ _Andrew Howroyd_, Jan 14 2022
%Y A139622 Row sums are A139627.
%Y A139622 Cf. A136564, A139621, A143841, A350489, A350753.
%K A139622 nonn,tabl
%O A139622 1,5
%A A139622 _Benoit Jubin_, May 01 2008
%E A139622 More terms from _R. J. Mathar_, Aug 11 2017
%E A139622 Terms a(34) and beyond from _Andrew Howroyd_, Jan 14 2022