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A350788
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Irregular triangle read by rows: T(n,k) is the number of partial functions on [n] such that the sizes of the preimages of the individual elements in the range form the k-th partition in the class of all partitions listed in Abramowitz and Stegun order, n>=0, 0<=k<=A000070(n).
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0
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1, 1, 1, 1, 4, 2, 2, 1, 9, 9, 18, 3, 18, 6, 1, 16, 24, 72, 16, 144, 96, 4, 48, 36, 144, 24, 1, 25, 50, 200, 50, 600, 600, 25, 400, 300, 1800, 600, 5, 100, 200, 600, 900, 1200, 120, 1, 36, 90, 450, 120, 1800, 2400, 90, 1800, 1350, 10800, 5400, 36, 900, 1800, 7200, 10800, 21600, 4320, 6, 180, 450, 1800, 300, 7200, 7200, 1800, 16200, 10800, 720
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OFFSET
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0,5
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COMMENTS
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Row sums are (n+1)^n = A000169(n+1).
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LINKS
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EXAMPLE
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1,
1, 1,
1, 4, 2, 2,
1, 9, 9, 18, 3, 18, 6,
1, 16, 24, 72, 16, 144, 96, 4, 48, 36, 144, 24
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MATHEMATICA
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g[n_, list_] := Multinomial @@ Join[{n - Length[list]}, Table[Count[list, i], {i, 1, n}]]* Multinomial @@ Join[{n - Total[list]}, list]; Table[Map[g[nn, #] &,
Level[Table[IntegerPartitions[k], {k, 0, nn}], {2}]], {nn, 0, 5}] // Grid
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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