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 A369397 #7 Jan 22 2024 13:02:15
%S A369397 1,1,5,157,26345,18218521,47136254765,451286947588597,
%T A369397 16264532016440908625,2253156851039460378774961,
%U A369397 1219026648017155982267265596885,2601923405098893502520360223043594957,22040885615442635622424409144799379027505465
%N A369397 Number of binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is an equivalence relation.
%C A369397 Equivalently, a(n) is the number of binary relations R on [n] such that the Frobenius normal form has no 0-blocks on the diagonal and all off diagonal blocks are 0-blocks.
%H A369397 D. A. Gregory, S. Kirkland, and N. J. Pullman, <a href="https://doi.org/10.1016/0024-3795(93)90323-G">Power convergent Boolean matrices</a>, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117.
%H A369397 S. Schwarz, <a href="http://dx.doi.org/10.21136/CMJ.1970.100989">On the semigroup of binary relations on a finite set </a>, Czechoslovak Mathematical Journal, 1970.
%F A369397 E.g.f.: exp(s(2x)-x) where s(x) is the e.g.f. for A003030.
%t A369397 nn = 12; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"],
%t A369397 Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]];
%t A369397 Table[n!, {n, 0, nn}] CoefficientList[Series[Exp [s[2 x] - x], {x, 0, nn}], x]
%Y A369397 Cf. A366866 (binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is a quasiorder), A365534, A366218, A365590, A355612, A365593, A366252, A366350, A366218.
%K A369397 nonn
%O A369397 0,3
%A A369397 _Geoffrey Critzer_, Jan 22 2024