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Triangular array read by rows. T(n,k) is the number of regular elements in the semigroup of all binary relations on [n] that have rank k, n>=0, 0<=k<=n.
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%I #27 May 18 2023 10:41:37

%S 1,1,1,1,9,6,1,49,306,114,1,225,8550,26376,5256,1,961,194850,3311250,

%T 4669200,507720

%N Triangular array read by rows. T(n,k) is the number of regular elements in the semigroup of all binary relations on [n] that have rank k, n>=0, 0<=k<=n.

%H K. K.-H. Butler and G. Markowsky, <a href="https://www.koreascience.or.kr/article/JAKO197225748110925.pdf">The Number of Maximal Subgroups of the Semigroup of Binary Relations</a>, Kyungpook Math. J. Vol 12, June 1972.

%e 1;

%e 1, 1;

%e 1, 9, 6;

%e 1, 49, 306, 114;

%e 1, 225, 8550, 26376, 5256;

%e 1, 961, 194850, 3311250, 4669200, 507720;

%e ...

%Y Cf. A354279 (row sums), A003425 (main diagonal), A060867 (column k=1), A354741.

%K nonn,tabl,more

%O 0,5

%A _Geoffrey Critzer_, May 17 2023