A352399 Triangular array read by rows: T(n,k) is the number of partial order relations on [n] that have exactly k components, n>=0, 0<=k<=n.

1, 0, 1, 0, 2, 1, 0, 12, 6, 1, 0, 146, 60, 12, 1, 0, 3060, 970, 180, 20, 1, 0, 101642, 24180, 3750, 420, 30, 1, 0, 5106612, 901334, 110040, 10990, 840, 42, 1, 0, 377403266, 49347228, 4567976, 376320, 27020, 1512, 56, 1, 0, 40299722580, 3923052354, 269812620, 17322648, 1071000, 58716, 2520, 72, 1

Offset: 0

Author

Geoffrey Critzer, Jul 05 2022

Keywords

• nonn
• tabl

Examples

			Triangle T(n,k) begins:
  1;
  0,    1;
  0,    2,   1;
  0,   12,   6,   1;
  0,  146,  60,  12,  1;
  0, 3060, 970, 180, 20, 1;
  ...
		

Crossrefs

Cf. A001927 (column 1), A001035 (row sums), A046908.

Programs

Mathematica

nn = 8; 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[A[x]^y, {x, 0, nn}], {x, y}])[[i]], i], {i, 1, nn}] // Grid

Formula

E.g.f.: A(x)^y where A(x) is the e.g.f. for A001035.