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A089759
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Table T(n,k), 0<=k, 0<=n, read by antidiagonals, defined by T(n,k) = (k*n)! / (n!)^k.
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16
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 6, 1, 1, 1, 24, 90, 20, 1, 1, 1, 120, 2520, 1680, 70, 1, 1, 1, 720, 113400, 369600, 34650, 252, 1, 1, 1, 5040, 7484400, 168168000, 63063000, 756756, 924, 1, 1, 1, 40320, 681080400, 137225088000, 305540235000, 11732745024, 17153136, 3432, 1, 1
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OFFSET
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0,8
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COMMENTS
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T(n,k) is the number of lattice paths from {n}^k to {0}^k using steps that decrement one component by 1. - Alois P. Heinz, May 06 2013
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LINKS
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EXAMPLE
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Row n=0: 1, 1, 1, 1, 1, 1, ... A000012
Row n=1: 1, 1, 2, 6, 24, 120, ... A000142
Row n=2: 1, 1, 6, 90, 2520, 113400, ... A000680
Row n=3: 1, 1, 20, 1680, 369600, 168168000, ... A014606
Row n=4: 1, 1, 70, 34650, 63063000, 305540235000, ... A014608
Row n=5: 1, 1, 252, 756756, 11732745024, 623360743125120, ... A014609
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MAPLE
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T:= (n, k)-> (k*n)!/(n!)^k:
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MATHEMATICA
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T[n_, k_] := (k*n)!/(n!)^k; Table[T[n-k, k], {n, 0, 10}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Dec 19 2015 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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