A243163 Triangle read by rows: T(n,k) = binomial(k,n-k)*binomial(n+2*k,n+k) /(n+k+1), n>=0, 0<=k<=n.

1, 0, 1, 0, 1, 3, 0, 0, 7, 12, 0, 0, 4, 45, 55, 0, 0, 0, 55, 286, 273, 0, 0, 0, 22, 546, 1820, 1428, 0, 0, 0, 0, 455, 4760, 11628, 7752, 0, 0, 0, 0, 140, 6120, 38760, 74613, 43263, 0, 0, 0, 0, 0, 3876, 67830, 302841, 480700, 246675, 0, 0, 0, 0, 0, 969, 65835

Offset: 0

Author

Peter Luschny, May 31 2014

Keywords

• nonn
• tabl

Examples

			                               1;
                              0, 1;
                            0, 1, 3;
                          0, 0, 7, 12;
                        0, 0, 4, 45, 55;
                     0, 0, 0, 55, 286, 273;
		

Crossrefs

Cf. A001764, A002293, A186997.

Programs

Maple

T := (n, k) -> binomial(k,n-k)*binomial(n+2*k,n+k)/(n+k+1);
seq(print(seq(T(n,k), k=0..n)), n=0..10);

Formula

T(n, n) = A001764(n).

T(2*n,n) = A002293(n).

Sum_{k=0..n} T(n, k) = A186997(n).