A050163 T(n, k) = S(2n+2, n+2, k+2) for 0<=k<=n and n >= 0, array S as in A050157.

1, 3, 4, 9, 14, 15, 28, 48, 55, 56, 90, 165, 200, 209, 210, 297, 572, 726, 780, 791, 792, 1001, 2002, 2639, 2912, 2989, 3002, 3003, 3432, 7072, 9620, 10880, 11320, 11424, 11439, 11440, 11934, 25194, 35190, 40698, 42942, 43605

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• tabl

Examples

			Triangle starts:
                                1
                              3, 4
                           9, 14, 15
                         28, 48, 55, 56
                     90, 165, 200, 209, 210
                  297, 572, 726, 780, 791, 792
            1001, 2002, 2639, 2912, 2989, 3002, 3003
		

Crossrefs

T(n, 0) = A000245(n+1).

T(n, 1) = A002057(n).

T(n, n) = A001791(n+1).

Row sums are A000531(n+1).

Cf. A050155, A050157.

Programs

Maple

A050163 := (n, k) -> binomial(2*n+2, n) - binomial(2*n+2, n+k+3):
seq(seq(A050163(n,k), k=0..n), n=0..8); # Peter Luschny, Dec 21 2017

Formula

T(n, k) = Sum_{0<=j<=k} t(n, j), array t as in A050155.

T(n, k) = binomial(2*n+2, n) - binomial(2*n+2, n+k+3). - Peter Luschny, Dec 21 2017