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 A369397 Number of binary relations R on [n] such that the (unique) idempotent in {R,R^2,R^3,...} is an equivalence relation. 0
 1, 1, 5, 157, 26345, 18218521, 47136254765, 451286947588597, 16264532016440908625, 2253156851039460378774961, 1219026648017155982267265596885, 2601923405098893502520360223043594957, 22040885615442635622424409144799379027505465 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Table of n, a(n) for n=0..12. D. A. Gregory, S. Kirkland, and N. J. Pullman, Power convergent Boolean matrices, Linear Algebra and its Applications, Volume 179, 15 January 1993, Pages 105-117. S. Schwarz, On the semigroup of binary relations on a finite set , Czechoslovak Mathematical Journal, 1970. FORMULA E.g.f.: exp(s(2x)-x) where s(x) is the e.g.f. for A003030. MATHEMATICA nn = 12; strong =Select[Import["https://oeis.org/A003030/b003030.txt", "Table"], Length@# == 2 &][[All, 2]]; s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]]; Table[n!, {n, 0, nn}] CoefficientList[Series[Exp [s[2 x] - x], {x, 0, nn}], x] CROSSREFS 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. Sequence in context: A009082 A156134 A183263 * A155208 A321529 A156486 Adjacent sequences: A369394 A369395 A369396 * A369398 A369399 A369400 KEYWORD nonn AUTHOR Geoffrey Critzer, Jan 22 2024 STATUS approved

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Last modified May 27 02:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)