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A132339 Array read by antidiagonals: see formula line for definition. 5

%I

%S 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,

%T 0,0,-2,-110,-660,-660,-110,-2,0,0,2,182,2002,4290,2002,182,2,0,0,-2,

%U -280,-5096,-20020,-20020,-5096,-280,-2,0,0,2,408,11424,74256,136136,74256

%N Array read by antidiagonals: see formula line for definition.

%H G. Kreweras, <a href="http://www.numdam.org/numdam-bin/item?id=BURO_1965__6__9_0">Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers</a>, Cahiers du Bureau Universitaire de Recherche Opérationnelle}, Institut de Statistique, Université de Paris, 6 (1965), circa p. 82.

%F A(n,k) = 2(-1)^(n+k) (n+k-1)! (2n+2k-3)! / ( n! k! (2n-1)! (2k-1)! ), n >= 0, k >= 0.

%e Array begins:

%e 1 -1 0 0 0 0 0 0 ...

%e -1 2 -2 2 -2 2 -2 2 ...

%e 0 -2 10 -28 60 -110 ...

%e 0 2 -28 168 -660 2002 ...

%e ...

%t 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 *)

%Y Rows give A006331-A006334. Main diagonal is A132341.

%K sign,tabl,easy

%O 0,5

%A _N. J. A. Sloane_, Nov 08 2007

%E More terms from _Max Alekseyev_, Sep 12 2009

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Last modified April 12 08:50 EDT 2021. Contains 342912 sequences. (Running on oeis4.)