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%I #13 Jun 29 2023 17:00:47
%S 1,1,4,30,384,7560,228960,10306800,685399680,66490865280,
%T 9316160179200,1866087527673600,529244914160793600,
%U 210621677079215001600,116661392964364363315200,89281569344544938769408000,93799600948326479830880256000
%N n! times the number of posets with n unlabeled elements.
%C Let H be Green's H relation on the semigroup of binary relations on [n]. Then a(n) is the number of elements that are H-related to a poset.
%C There are A000112(n) D-classes containing the nonsingular relations. There are A001035(n) L-classes in these D-classes. Each such L-class contains exactly one idempotent relation (which is necessarily a poset).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Green's_relations">Green's relations</a>
%F a(n) = A000142(n)*A000112(n).
%t nn = 10; A000112 = Cases[Import["https://oeis.org/A000112/b000112.txt",
%t "Table"], {_, _}][[All, 2]];Range[0, 16]! Table[A000112[[i]], {i, 1, 17}]
%Y Cf. A003425, A000142, A001035, A000112.
%K nonn
%O 0,3
%A _Geoffrey Critzer_, Jun 27 2023