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A132339
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Array read by antidiagonals: see formula line for definition.
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5
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1, -1, -1, 0, 2, 0, 0, -2, -2, 0, 0, 2, 10, 2, 0, 0, -2, -28, -28, -2, 0, 0, 2, 60, 168, 60, 2, 0, 0, -2, -110, -660, -660, -110, -2, 0, 0, 2, 182, 2002, 4290, 2002, 182, 2, 0, 0, -2, -280, -5096, -20020, -20020, -5096, -280, -2, 0, 0, 2, 408, 11424, 74256, 136136, 74256
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history;
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OFFSET
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0,5
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LINKS
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Table of n, a(n) for n=0..61.
G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du Bureau Universitaire de Recherche Opérationnelle}, Institut de Statistique, Université de Paris, 6 (1965), circa p. 82.
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FORMULA
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A(n,k) = 2(-1)^(n+k) (n+k-1)! (2n+2k-3)! / ( n! k! (2n-1)! (2k-1)! ), n >= 0, k >= 0.
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EXAMPLE
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Array begins:
1 -1 0 0 0 0 0 0 ...
-1 2 -2 2 -2 2 -2 2 ...
0 -2 10 -28 60 -110 ...
0 2 -28 168 -660 2002 ...
...
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MATHEMATICA
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Flatten[{{1}, {-1, -1}}~Join~Table[(2 (-1)^(# + k) (# + k - 1)! (2 # + 2 k - 3)!)/(#! k! (2 # - 1)! (2 k - 1)!) &@(n - k), {n, 2, 10}, {k, 0, n}]] (* Michael De Vlieger, Mar 26 2016 *)
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CROSSREFS
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Rows give A006331-A006334. Main diagonal is A132341.
Sequence in context: A122071 A099766 A194947 * A137676 A238130 A238707
Adjacent sequences: A132336 A132337 A132338 * A132340 A132341 A132342
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KEYWORD
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sign,tabl,easy
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AUTHOR
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N. J. A. Sloane, Nov 08 2007
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EXTENSIONS
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More terms from Max Alekseyev, Sep 12 2009
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STATUS
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approved
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