

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
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OFFSET

0,3


COMMENTS

Equivalently, a(n) is the number of binary relations R on [n] such that the Frobenius normal form has no 0blocks on the diagonal and all off diagonal blocks are 0blocks.


LINKS



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.


KEYWORD

nonn


AUTHOR



STATUS

approved



