A335987
Triangular array read by rows: T(n,k) is the number of labeled quasi-orders on [n] that are composed of exactly k irreducible components n>=0, 0<=k<=n.
Original entry on oeis.org
1, 0, 1, 0, 2, 2, 0, 11, 12, 6, 0, 147, 112, 72, 24, 0, 3412, 1910, 1020, 480, 120, 0, 121553, 52184, 21870, 9600, 3600, 720, 0, 6353629, 2101540, 693672, 254520, 96600, 30240, 5040, 0, 476850636, 120988214, 31163496, 9289728, 3116400, 1048320, 282240, 40320
Offset: 0
1;
0, 1;
0, 2, 2;
0, 11, 12, 6;
0, 147, 112, 72, 24;
0, 3412, 1910, 1020, 480, 120;
...
-
nn = 9; A[x_] := Total[Cases[Import["https://oeis.org/A000798/b000798.txt",
"Table"], {, }][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 19}]];
Table[Take[(Range[0, nn]! CoefficientList[Series[1/(1 - y (1 - 1/A[x])), {x, 0, nn}], {x, y}])[[i]], i], {i, 1, nn}] // Grid
A046906
Number of connected irreducible posets with n labeled points.
Original entry on oeis.org
1, 1, 0, 0, 24, 1080, 52440, 3281880, 277953144, 32418855000, 5239070305080, 1173944480658840, 363936227764858584, 155521768202208047640, 91218870039317505477720, 73113879800794757415243480, 79743817918540500914682249144, 117883366412734188786535902826200, 235329353612778837110901775412557560
Offset: 0
- J. A. Wright, There are 718 6-point topologies, quasi-orderings and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
A003431 gives isomorphism classes of these posets.
-
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 *)
Showing 1-2 of 2 results.