A363911 n! times the number of posets with n unlabeled elements.

1, 1, 4, 30, 384, 7560, 228960, 10306800, 685399680, 66490865280, 9316160179200, 1866087527673600, 529244914160793600, 210621677079215001600, 116661392964364363315200, 89281569344544938769408000, 93799600948326479830880256000

Offset: 0

Author

Geoffrey Critzer, Jun 27 2023

Keywords

• nonn

Comments

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.

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).

Links

• Wikipedia, Green's relations

Crossrefs

Cf. A003425, A000142, A001035, A000112.

Programs

Mathematica

nn = 10; A000112 = Cases[Import["https://oeis.org/A000112/b000112.txt",
    "Table"], {, }][[All, 2]];Range[0, 16]! Table[A000112[[i]], {i, 1, 17}]

Formula

a(n) = A000142(n)*A000112(n).