This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360984 #34 Mar 05 2023 11:27:39 %S A360984 1,1,1,1,6,4,1,27,66,29,1,108,780,1116,355,1,405,8020,29250,28405, %T A360984 6942,1,1458,76110,649260,1460425,1068576,209527 %N A360984 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 A360984 T(n,n) = A245767(n,n) = A000798(n). %F A360984 T(n,n-1) = A245767(n,n-1). %F A360984 T(n,1) = n*Sum_k Sum_j binomial(n-1,k)*binomial(n-1-k,j) = A027471(n+1). %F A360984 E.g.f. for column 1 is x*exp(x)^3. %F A360984 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 A360984 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 A360984 Triangle T(n,k) begins: %e A360984 1; %e A360984 1, 1; %e A360984 1, 6, 4; %e A360984 1, 27, 66, 29; %e A360984 1, 108, 780, 1116, 355; %e A360984 1, 405, 8020, 29250, 28405, 6942; %e A360984 ... %Y A360984 Cf. A121337 (row sums), A000798 (main diagonal). %Y A360984 Cf. A245767, A027471 (column 1). %K A360984 nonn,hard,tabl,more %O A360984 0,5 %A A360984 _Geoffrey Critzer_, Feb 27 2023 %E A360984 Rows 5 and 6 added by _Geoffrey Critzer_, Mar 05 2023