A067802 Triangle read by rows: T(n, k) = binomial(2*n+1, n-k)^2*(2*k+1)/(2*n+1).

1, 3, 1, 20, 15, 1, 175, 189, 35, 1, 1764, 2352, 720, 63, 1, 19404, 29700, 12375, 1925, 99, 1, 226512, 382239, 196625, 44044, 4212, 143, 1, 2760615, 5010005, 3006003, 869505, 124215, 8085, 195, 1, 34763300, 66745536, 45048640, 15767024, 2998800, 299200, 14144, 255, 1

Offset: 0

Author

Henry Bottomley, Feb 07 2002

Keywords

• nonn
• tabl

Examples

			Triangle starts:
  [0]      1
  [1]      3,      1
  [2]     20,     15,      1
  [3]    175,    189,     35,     1
  [4]   1764,   2352,    720,    63,    1
  [5]  19404,  29700,  12375,  1925,   99,   1
  [6] 226512, 382239, 196625, 44044, 4212, 143, 1
		

Crossrefs

First column is A000891.

Cf. A034869, A039599, A002894 (row sums).

Programs

Maple

T := (n, k) -> binomial(2*n+1, n-k)^2*(2*k+1)/(2*n+1):
seq(seq(T(n, k), k = 0..n), n = 0..8);  # Peter Luschny, Dec 07 2024

Formula

T(n, k) = A034869(2n+1, k) * A039599(n, k).