A354615 Triangular array read by rows: T(n,k) is the number of labeled posets on [n] that are composed of exactly k irreducible posets, n >= 0, 0 <= k <= n.

1, 0, 1, 0, 1, 2, 0, 7, 6, 6, 0, 97, 62, 36, 24, 0, 2251, 1110, 510, 240, 120, 0, 80821, 30902, 11340, 4440, 1800, 720, 0, 4305127, 1273566, 369726, 119280, 42000, 15120, 5040, 0, 332273257, 75831422, 17192196, 4476024, 1335600, 433440, 141120, 40320

Offset: 0

Author

Geoffrey Critzer, Jul 08 2022

Keywords

• nonn
• tabl

Examples

			  1;
  0,    1;
  0,    1,    2;
  0,    7,    6,   6;
  0,   97,   62,  36,  24;
  0, 2251, 1110, 510, 240, 120;
  ...
		

Crossrefs

Cf. A046908 (column k=1), A001035 (row sums), A000142 (main diagonal).

Programs

Mathematica

nn = 9; A[x_] := Total[Cases[Import["https://oeis.org/A001035/b001035.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}]

Formula

E.g.f.: 1/(1-y*(1-1/A(x))) where A(x) is the e.g.f. for A001035.