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%I #12 Mar 14 2020 10:32:20
%S 1,2,3,3,12,20,12,20,120,210,10,120,210,1680,3024,60,105,1680,3024,
%T 30240,55440,35,840,1512,30240,55440,665280,1235520,280,504,15120,
%U 27720,665280,1235520,17297280,32432400,126,5040,9240,332640,617760,17297280,32432400,518918400,980179200
%N Triangle read by rows, T(n,k) = (n+k+1)! / ([(n-k)/2]! * [(n+k+2)/2]!) with [.] the floor function, for n>=0 and 0<=k<=n.
%e Triangle starts:
%e [0] [1]
%e [1] [2, 3]
%e [2] [3, 12, 20]
%e [3] [12, 20, 120, 210]
%e [4] [10, 120, 210, 1680, 3024]
%e [5] [60, 105, 1680, 3024, 30240, 55440]
%e [6] [35, 840, 1512, 30240, 55440, 665280, 1235520]
%e [7] [280, 504, 15120, 27720, 665280, 1235520, 17297280, 32432400]
%t Table[(n+k+1)!/(Floor[(n-k)/2]!Floor[(n+k+2)/2]!),{n,0,10},{k,0,n}]// Flatten (* _Harvey P. Dale_, Mar 27 2019 *)
%o (Sage)
%o def T(n, k):
%o return factorial(n+k+1)//(factorial((n-k)//2)*factorial((n+k+2)//2))
%o for n in (0..7): print([T(n,k) for k in (0..n)])
%Y Cf. A001813 (subdiagonal), A006963 (main diagonal), A212303 (first column).
%K nonn,tabl
%O 0,2
%A _Peter Luschny_, Jul 20 2016
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