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%I #11 Dec 08 2024 12:54:50
%S 1,1,2,2,3,12,6,8,20,120,24,30,60,210,1680,120,144,252,672,3024,30240,
%T 720,840,1344,3024,10080,55440,665280,5040,5760,8640,17280,47520,
%U 190080,1235520,17297280,40320,45360,64800,118800,285120,926640,4324320,32432400,518918400
%N Triangle read by rows: T(n, k) = (n - k)!*(n + k)!/n!.
%e Triangle starts:
%e [0] 1;
%e [1] 1, 2;
%e [2] 2, 3, 12;
%e [3] 6, 8, 20, 120;
%e [4] 24, 30, 60, 210, 1680;
%e [5] 120, 144, 252, 672, 3024, 30240;
%e [6] 720, 840, 1344, 3024, 10080, 55440, 665280;
%p T := (n, k) -> (n-k)!*(n+k)!/n!: seq(seq(T(n, k), k= 0..n), n = 0..8);
%Y Cf. A000142, A001813.
%K nonn,tabl,new
%O 0,3
%A _Peter Luschny_, Dec 08 2024