|
%I #83 Jan 06 2023 13:48:29
%S 1,0,1,0,2,2,0,11,12,6,0,147,112,72,24,0,3412,1910,1020,480,120,0,
%T 121553,52184,21870,9600,3600,720,0,6353629,2101540,693672,254520,
%U 96600,30240,5040,0,476850636,120988214,31163496,9289728,3116400,1048320,282240,40320
%N 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.
%H Alois P. Heinz, <a href="/A335987/b335987.txt">Rows n = 0..18, flattened</a>
%F E.g.f.: 1/(1 - y*(1 - 1/A(x))) where A(x) is the e.g.f. for A000798.
%e 1;
%e 0, 1;
%e 0, 2, 2;
%e 0, 11, 12, 6;
%e 0, 147, 112, 72, 24;
%e 0, 3412, 1910, 1020, 480, 120;
%e ...
%t nn = 9; A[x_] := Total[Cases[Import["https://oeis.org/A000798/b000798.txt",
%t "Table"], {_, _}][[All, 2]]*Table[x^(i - 1)/(i - 1)!, {i, 1, 19}]];
%t 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
%Y Cf. A000798 (row sums), A046912 (column k=1), A000142 (main diagonal), A354615.
%K nonn,tabl
%O 0,5
%A _Geoffrey Critzer_, Jul 10 2022
|
