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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
E.g.f.: 1/(1 - y*(1 - 1/A(x))) where A(x) is the e.g.f. for A000798.
EXAMPLE
1;
0, 1;
0, 2, 2;
0, 11, 12, 6;
0, 147, 112, 72, 24;
0, 3412, 1910, 1020, 480, 120;
...
MATHEMATICA
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
CROSSREFS
Cf. A000798 (row sums), A046912 (column k=1), A000142 (main diagonal), A354615.
Sequence in context: A268652 A111810 A019265 * A285539 A285783 A364240
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jul 10 2022
STATUS
approved

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Last modified February 21 10:38 EST 2024. Contains 370228 sequences. (Running on oeis4.)