A046912 -id:A046912 - cp's OEIS frontend

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.

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

Geoffrey Critzer, Jul 10 2022

			  1;
  0,    1;
  0,    2,    2;
  0,   11,   12,    6;
  0,  147,  112,   72,  24;
  0, 3412, 1910, 1020, 480, 120;
  ...

Alois P. Heinz, Rows n = 0..18, flattened

Cf. A000798 (row sums), A046912 (column k=1), A000142 (main diagonal), A354615.

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

E.g.f.: 1/(1 - y*(1 - 1/A(x))) where A(x) is the e.g.f. for A000798.

A046911 Number of isomorphism classes of irreducible quasiorders with n labeled points.

Original entry on oeis.org

1, 1, 2, 4, 14, 62, 373, 2722

Offset: 0

John A. Wright

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

J. A. Wright, Letter to N. J. A. Sloane, Apr 06 1972, listing 18 sequences

Cf. A046912.

cp's OEIS Frontend

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.

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