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A352399
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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.
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1
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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
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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E.g.f.: A(x)^y where A(x) is the e.g.f. for A001035.
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EXAMPLE
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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;
...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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