A046906 Number of connected irreducible posets with n labeled points.

1, 1, 0, 0, 24, 1080, 52440, 3281880, 277953144, 32418855000, 5239070305080, 1173944480658840, 363936227764858584, 155521768202208047640, 91218870039317505477720, 73113879800794757415243480, 79743817918540500914682249144, 117883366412734188786535902826200, 235329353612778837110901775412557560

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

• S. R. Finch, Series-parallel networks
• S. R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]
• J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences
• Index entries for sequences related to posets

Crossrefs

A003431 gives isomorphism classes of these posets.

Programs

Mathematica

nn = 18; A[x_] := Total[Cases[Import["https://oeis.org/A001035/b001035.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 09 2022 *)

Formula

From Geoffrey Critzer, Jul 09 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 A001035.

a(n) = A001927(n) - Sum_{k>=2} A354615(n,k). (End)

Extensions

a(8)-a(18) from Geoffrey Critzer, Jul 09 2022

a(0) changed to 1 by Geoffrey Critzer, Jul 10 2022