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A350610 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= (n-1)*(n-2)/2) = number of weakly connected subdigraphs of the transitive tournament on n nodes that have k arcs.

%I A350610 #20 Jan 27 2022 16:41:55
%S A350610 1,1,1,3,1,6,15,9,1,10,45,120,162,109,27,1,15,105,455,1365,2755,3738,
%T A350610 3353,1889,600,81,1,21,210,1330,5985,20349,52764,104726,159351,185155,
%U A350610 162455,105436,48881,15255,2862,243,1,28,378,3276,20475,98280,376740,1173564,2995480,6295857,10925190,15658609,18498220,17926289,14138445,8968823,4498534,1740117,499834,100225,12501,729
%N A350610 Irregular triangle read by rows: T(n,k) (n >= 1, 0 <= k <= (n-1)*(n-2)/2) = number of weakly connected subdigraphs of the transitive tournament on n nodes that have k arcs.
%C A350610 The sum of row n is A350608(n).
%C A350610 For references and links see A350608.
%H A350610 Don Knuth, <a href="/A350610/b350610.txt">Rows n = 1..16, flattened</a>
%H A350610 Don Knuth, <a href="/A350610/a350610.txt">The first 16 rows.</a>
%e A350610 For example, when n=4, the 31 weakly connected graphs have respectively 1, 6, 15, 9 cases with 0, 1, 2, and 3 arcs (as in the example given for A350608).
%e A350610 Triangle T(n,k) begins:
%e A350610   1;
%e A350610   1;
%e A350610   1,  3;
%e A350610   1,  6,  15,   9;
%e A350610   1, 10,  45, 120,  162,  109,   27;
%e A350610   1, 15, 105, 455, 1365, 2755, 3738, 3353, 1889, 600, 81;
%e A350610   ...
%Y A350610 Cf. A350608, A350609.
%K A350610 nonn,tabf
%O A350610 1,4
%A A350610 _Don Knuth_, Jan 16 2022