A046910 Number of connected irreducible quasiorders with n labeled points.

1, 1, 1, 1, 25, 1321, 70201, 4542721, 384969649, 44087846545, 6926924885881, 1503058888234201, 451117640363382697, 186980881340749198561, 106678398214255092939169, 83440038893764124092029601, 89093417035281194970121062073, 129323858612953057624127147727913, 254190262374139251098507525465587609

Offset: 0

Author

John A. Wright

Keywords

• nonn

Links

• John A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
• John A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences

Crossrefs

Cf. A046909, A335987, A000798, A001929.

Programs

Mathematica

nn = 18; A[x_] :=Total[Cases[Import["https://oeis.org/A000798/b000798.txt",
      "Table"], {, }][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 19}]];
Range[0, nn]! CoefficientList[Series[1 + Log[A[x]] - A[x] (1 - 1/A[x])^2, {x, 0, nn}], x] (* Geoffrey Critzer, Jul 10 2022 *)

Formula

From Geoffrey Critzer, Jul 10 2022: (Start)

E.g.f.: 1 + log(A(x)) - A(x)*(1 - 1/A(x))^2 where A(x) is the e.g.f. for A000798.

a(n) = A001929(n) - Sum_{k>=2} A335987(n,k). (End)

Extensions

a(8)-a(18) from Geoffrey Critzer, Jul 10 2022