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 A366218 #14 Oct 05 2023 08:38:04
%S A366218 1,1,4,149,26177,18211032,47135163595
%N A366218 Number of convergent binary relations on [n] (A365534) that converge to an equivalence relation (A000110).
%C A366218 Equivalently, a(n) is the number of Boolean relation matrices whose Frobenius normal form is such that all the diagonal blocks are primitive (A070322) and all the off diagonal blocks are 0-blocks. See Gregory, Kirkland, Pullman.
%C A366218 The limit of a convergent binary relation R is an equivalence relation iff every vertex and every edge in G(R) is on a cycle, where G(R) is the directed graph with loops associated to R. See Corollary to Theorem 1 in Rosenblatt.
%H A366218 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, pp. 105-117.
%H A366218 D. Rosenblatt, <a href="https://nvlpubs.nist.gov/nistpubs/jres/67B/jresv67Bn4p249_A1b.pdf">On the graphs of finite Boolean relation matrices</a>, Journal of Research of the National Bureau of Standards, 67B No. 4, 1963.
%F A366218 E.g.f.: exp(p(x)-1) where p(x) is the e.g.f. for A070322.
%t A366218 nn = 13; B[n_] := 2^Binomial[n, 2] n!; primitive = Select[Import["https://oeis.org/A070322/b070322.txt", "Table"],
%t A366218 Length@# == 2 &][[All, 2]];pr[x_] := Total[primitive Table[x^i/i!, {i, 0, 6}]];Table[n!, {n, 0, nn}] CoefficientList[Series[Exp[pr[x] - 1], {x, 0, nn}], x]
%Y A366218 Cf. A070322, A365534, A000110.
%K A366218 nonn,more
%O A366218 0,3
%A A366218 _Geoffrey Critzer_, Oct 04 2023