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%I #34 Mar 05 2023 11:27:39
%S 1,1,1,1,6,4,1,27,66,29,1,108,780,1116,355,1,405,8020,29250,28405,
%T 6942,1,1458,76110,649260,1460425,1068576,209527
%N Triangular array read by rows. T(n,k) is the number of idempotent Boolean relation matrices on [n] with exactly k reflexive points, n >= 0, 0 <= k <= n.
%F T(n,n) = A245767(n,n) = A000798(n).
%F T(n,n-1) = A245767(n,n-1).
%F T(n,1) = n*Sum_k Sum_j binomial(n-1,k)*binomial(n-1-k,j) = A027471(n+1).
%F E.g.f. for column 1 is x*exp(x)^3.
%F E.g.f. for column 2 is x^2/2*exp(x)^3 + x^2*exp(x)^6 + x^2/2*exp(x)^7.
%F E.g.f. for column 3 is x^3/3!*exp(x)^15 + x^3/3!*exp(x)^3 + x^3*exp(x)^10 + x^3*exp(x)^12 + x^3/2!*exp(x)^7 + 2*x^3/2!*exp(x)^6 + 2*x^3/2*exp(x)^12.
%e Triangle T(n,k) begins:
%e 1;
%e 1, 1;
%e 1, 6, 4;
%e 1, 27, 66, 29;
%e 1, 108, 780, 1116, 355;
%e 1, 405, 8020, 29250, 28405, 6942;
%e ...
%Y Cf. A121337 (row sums), A000798 (main diagonal).
%Y Cf. A245767, A027471 (column 1).
%K nonn,hard,tabl,more
%O 0,5
%A _Geoffrey Critzer_, Feb 27 2023
%E Rows 5 and 6 added by _Geoffrey Critzer_, Mar 05 2023
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