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A259101
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Square array read by antidiagonals arising in the enumeration of corners.
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1
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1, 2, 2, 5, 16, 5, 14, 91, 91, 14, 42, 456, 936, 456, 42, 132, 2145, 7425, 7425, 2145, 132, 429, 9724, 50765, 85800, 50765, 9724, 429, 1430, 43043, 315315, 805805, 805805, 315315, 43043, 1430, 4862, 187408, 1831648, 6584032, 9962680, 6584032, 1831648, 187408, 4862, 16796, 806208, 10127988, 48674808, 103698504, 103698504, 48674808, 10127988, 806208, 16796
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OFFSET
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0,2
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COMMENTS
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See Kreweras (1979) for precise definition.
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LINKS
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FORMULA
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Kreweras gives an explicit formula for the general term (see bottom display on page 291).
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EXAMPLE
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The first few antidiagonals are:
1,
2, 2,
5, 16, 5,
14, 91, 91, 14,
42, 456, 936, 456, 42,
132, 2145, 7425, 7425, 2145, 132,
...
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MATHEMATICA
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a[x_, y_] := (2(2x+2y+1)!(x^2+3x*y+y^2+4x+4y+3)) / (x!(x+1)!y!(y+1)!(x+y+1)(x+y+2)(x+y+3));
Table[Table[a[x-y, y], {y, 0, x}] // Reverse, {x, 0, 9}] // Flatten (* Jean-François Alcover, Aug 11 2017 *)
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CROSSREFS
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The first row and column of the array are the Catalan numbers A000108.
The second row and column are A214824.
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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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