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A123163 Triangle read by rows: binomial[(n-m)^2,m^2]. 1

%I

%S 1,1,0,1,1,0,1,4,0,0,1,9,1,0,0,1,16,126,0,0,0,1,25,1820,1,0,0,0,1,36,

%T 12650,11440,0,0,0,0,1,49,58905,2042975,1,0,0,0,0,1,64,211876,

%U 94143280,2042975,0,0,0,0,0,1,81,635376,2054455634,7307872110,1,0,0,0,0,0

%N Triangle read by rows: binomial[(n-m)^2,m^2].

%F a(n,m) = (n^2 - 2*n*m + m^2)!/((m^2)!(n^2 - 2*n*m)!)

%e n\m | 0 1 2 3 4 5 6 7

%e ----+---------------------------------

%e 0 | 1;

%e 1 | 1, 0;

%e 2 | 1, 1, 0;

%e 3 | 1, 4, 0, 0;

%e 4 | 1, 9, 1, 0, 0;

%e 5 | 1, 16, 126, 0, 0, 0;

%e 6 | 1, 25, 1820, 1, 0, 0, 0;

%e 7 | 1, 36, 12650, 11440, 0, 0, 0, 0;

%t t[n_, m_] = (n^2 - 2*n*m + m^2)!/((m^2)!(n^2 - 2*n*m)!); a = Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]

%t Flatten[Table[Binomial[(n-m)^2,m^2],{n,0,10},{m,0,n}]] (* _Harvey P. Dale_, Aug 08 2012 *)

%Y Cf. A011973, A123165.

%K nonn,tabl

%O 0,8

%A _Roger L. Bagula_, Oct 02 2006

%E Edited by _N. J. A. Sloane_, Oct 04 2006

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Last modified August 7 11:08 EDT 2020. Contains 336275 sequences. (Running on oeis4.)