A050158 T(n, k) = S(2*n + 1, n, k + 1) for 0<=k<=n and n >= 0, array S as in A050157.

1, 2, 3, 5, 9, 10, 14, 28, 34, 35, 42, 90, 117, 125, 126, 132, 297, 407, 451, 461, 462, 429, 1001, 1430, 1638, 1703, 1715, 1716, 1430, 3432, 5070, 5980, 6330, 6420, 6434, 6435, 4862, 11934, 18122, 21930, 23630, 24174, 24293

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle starts:
                               1
                              2, 3
                            5, 9, 10
                         14, 28, 34, 35
                     42, 90, 117, 125, 126
                  132, 297, 407, 451, 461, 462
            429, 1001, 1430, 1638, 1703, 1715, 1716
		

Crossrefs

T(n, 0) = A000108(n+1).

T(n, 1) = A000245(n+1).

T(n, n) = A001700(n).

T(n,n-1) = A010763(n).

Row sums are A296770.

Cf. A039598, A050157.

Programs

Maple

A050158 := (n, k) ->  binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1):
seq(seq(A050158(n,k), k=0..n), n=0..6); # Peter Luschny, Dec 22 2017

Formula

T(n, k) = Sum_{0<=j<=k} t(n, j), array t as in A039598.

T(n, k) = binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1). Peter Luschny, Dec 22 2017