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A046906
Number of connected irreducible posets with n labeled points.
1
1, 1, 0, 0, 24, 1080, 52440, 3281880, 277953144, 32418855000, 5239070305080, 1173944480658840, 363936227764858584, 155521768202208047640, 91218870039317505477720, 73113879800794757415243480, 79743817918540500914682249144, 117883366412734188786535902826200, 235329353612778837110901775412557560
OFFSET
0,5
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.
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)
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 *)
CROSSREFS
A003431 gives isomorphism classes of these posets.
Sequence in context: A112011 A112010 A278650 * A130552 A374885 A160260
KEYWORD
nonn
AUTHOR
John A. Wright.
EXTENSIONS
a(8)-a(18) from Geoffrey Critzer, Jul 09 2022
a(0) changed to 1 by Geoffrey Critzer, Jul 10 2022
STATUS
approved