A275212 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.

1, 2, 3, 3, 12, 20, 12, 20, 120, 210, 10, 120, 210, 1680, 3024, 60, 105, 1680, 3024, 30240, 55440, 35, 840, 1512, 30240, 55440, 665280, 1235520, 280, 504, 15120, 27720, 665280, 1235520, 17297280, 32432400, 126, 5040, 9240, 332640, 617760, 17297280, 32432400, 518918400, 980179200

Offset: 0

Author

Peter Luschny, Jul 20 2016

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] [1]
[1] [2, 3]
[2] [3, 12, 20]
[3] [12, 20, 120, 210]
[4] [10, 120, 210, 1680, 3024]
[5] [60, 105, 1680, 3024, 30240, 55440]
[6] [35, 840, 1512, 30240, 55440, 665280, 1235520]
[7] [280, 504, 15120, 27720, 665280, 1235520, 17297280, 32432400]
		

Crossrefs

Cf. A001813 (subdiagonal), A006963 (main diagonal), A212303 (first column).

Programs

Mathematica

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 *)

Sage

def T(n, k):
    return factorial(n+k+1)//(factorial((n-k)//2)*factorial((n+k+2)//2))
for n in (0..7): print([T(n,k) for k in (0..n)])