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A368569 Irregular triangle read by rows: T(n,k) is the number of essential graphs with n nodes and k (directed or undirected) edges (n >= 1, 0 <= k <= n*(n-1)/2).

%I A368569 #51 Feb 07 2024 17:39:40
%S A368569 1,1,1,1,3,6,1,1,6,27,60,66,24,1,1,10,75,350,1120,2130,2595,1730,690,
%T A368569 80,1,1,15,165,1235,6930,27882,79825,162315,236490,245150,180936,
%U A368569 91560,29890,5190,240,1
%N A368569 Irregular triangle read by rows: T(n,k) is the number of essential graphs with n nodes and k (directed or undirected) edges (n >= 1, 0 <= k <= n*(n-1)/2).
%e A368569 Triangle T(n,k) (with n >= 1 and 0 <= k <= n*(n-1)/2) begins as follows:
%e A368569   1;
%e A368569   1,  1;
%e A368569   1,  3,  6,   1;
%e A368569   1,  6, 27,  60,   66,   24,    1;
%e A368569   1, 10, 75, 350, 1120, 2130, 2595, 1730, 690, 80, 1;
%e A368569   ...
%Y A368569 Row sums give A007984.
%Y A368569 Row lengths give A000124.
%Y A368569 Column k=1 is A000217.
%Y A368569 Column k=2 is A239568.
%K A368569 nonn,tabf,more
%O A368569 1,5
%A A368569 _Moritz Schauer_, Feb 06 2024