A301477 T(n,k) = Sum_{j=0..n-k} H(n,j)*2^k with H(n,k) = binomial(n,k)* hypergeom([-k/2, 1/2-k/2], [2-k+n], 4), for 0 <= k <= n, triangle read by rows.

1, 2, 2, 5, 6, 4, 13, 18, 16, 8, 35, 52, 56, 40, 16, 96, 150, 180, 160, 96, 32, 267, 432, 560, 568, 432, 224, 64, 750, 1246, 1708, 1904, 1680, 1120, 512, 128, 2123, 3600, 5152, 6160, 6048, 4736, 2816, 1152, 256, 6046, 10422, 15432, 19488, 20736, 18240, 12864, 6912, 2560, 512

Offset: 0

Author

Peter Luschny, Mar 22 2018

Keywords

• nonn
• tabl

Examples

			                               1
                              2, 2
                            5, 6, 4
                         13, 18, 16, 8
                       35, 52, 56, 40, 16
                   96, 150, 180, 160, 96, 32
                267, 432, 560, 568, 432, 224, 64
          750, 1246, 1708, 1904, 1680, 1120, 512, 128
      2123, 3600, 5152, 6160, 6048, 4736, 2816, 1152, 256
		

Crossrefs

Row sums are A126932, first column A005773, diagonal A000079.

Cf. A301475 (general case).

Programs

Maple

H := (n,k) -> binomial(n,k)*hypergeom([-k/2,1/2-k/2],[2-k+n], 4):
T := (n,k) -> add(simplify(H(n,j)*2^k), j=0..n-k):
seq(seq(T(n,k), k=0..n), n=0..9);

Mathematica

s={};For[n=0,n<13,n++,For[k=0,kDetlef Meya, Oct 03 2023 *)