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A123554 Triangle read by rows: T(n,k) = number of labeled loopless digraphs with n nodes and k arcs (n >= 1, 0 <= k <= n*(n-1)).

%I A123554 #23 Apr 20 2020 00:26:39
%S A123554 1,1,2,1,1,6,15,20,15,6,1,1,12,66,220,495,792,924,792,495,220,66,12,1,
%T A123554 1,20,190,1140,4845,15504,38760,77520,125970,167960,184756,167960,
%U A123554 125970,77520,38760,15504,4845,1140,190,20,1,1,30,435,4060,27405,142506,593775
%N A123554 Triangle read by rows: T(n,k) = number of labeled loopless digraphs with n nodes and k arcs (n >= 1, 0 <= k <= n*(n-1)).
%D A123554 J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 521.
%H A123554 G. C. Greubel, <a href="/A123554/b123554.txt">Table of n, a(n) for the first 25 rows, flattened</a>
%F A123554 T(n,k) = binomial(n*(n-1), k). - _Andrew Howroyd_, Apr 19 2020
%e A123554 Triangle begins:
%e A123554 1
%e A123554 1 2 1
%e A123554 1 6 15 20 15 6 1
%e A123554 1 12 66 220 495 792 924 792 495 220 66 12 1
%t A123554 Table[CoefficientList[Series[(1+x)^(2*Binomial[n,2]), {x,0,2*Binomial[n,2]}], x], {n,6}] (* _Geoffrey Critzer_, Nov 12 2011 *)
%o A123554 (PARI) T(n,k)={binomial(n*(n-1), k)}
%o A123554 {for(n=1, 5, for(k=0, n*(n-1), print1(T(n,k), ", ")); print)} \\ _Andrew Howroyd_, Apr 19 2020
%Y A123554 Row sums are A053763.
%Y A123554 Cf. A052283 (unlabeled analog).
%K A123554 nonn,tabf
%O A123554 1,3
%A A123554 _N. J. A. Sloane_, Nov 15 2006
%E A123554 More terms from _Vladeta Jovovic_, Nov 15 2006