A046908 Number of irreducible posets with n labeled points.

1, 1, 1, 7, 97, 2251, 80821, 4305127, 332273257, 36630174931, 5711638291981, 1249898984911567, 381230073532620577, 161042140788424003291, 93667063572594041040421, 74610767840852891620692727, 80997478506602342803118178457, 119313601058907927882431190269731, 237541348427311374857037021264415741

Offset: 0

Author

John A. Wright

Keywords

• nonn

References

• J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.

Links

• G. Brinkmann, B. D. McKay, Posets on up to 16 Points, Order 19 (2) (2002) 147-179 (Table III, up to 18 points)
• J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences
• Index entries for sequences related to posets

Crossrefs

Cf. A046907.

Programs

Mathematica

A001035 = Cases[Import["https://oeis.org/A001035/b001035.txt", "Table"], {, }][[All, 2]]; lg = Length[A001035];
B[x_] = Sum[A001035[[n + 1]] x^n/n!, {n, 0, lg - 1}];
A[x_] = 2 - 1/B[x];
CoefficientList[A[x] + O[x]^lg, x]*Range[0, lg - 1]! (* Jean-François Alcover, Jan 01 2020 *)

Formula

E.g.f.: A(x) = 2-1/B(x), where B(x) is e.g.f. of A001035. - Vladeta Jovovic, Jan 10 2006

Extensions

More terms from Vladeta Jovovic, Jan 10 2006

a(16)-a(18) from A001035 by Jean-François Alcover, Jan 01 2020