A299444 Triangle read by rows, T(n, k) = 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2) for n >= 0 and 0 <= k <= n.

1, 1, 2, 1, 5, 4, 1, 10, 16, 8, 1, 17, 49, 44, 16, 1, 26, 121, 182, 112, 32, 1, 37, 256, 593, 584, 272, 64, 1, 50, 484, 1616, 2368, 1712, 640, 128, 1, 65, 841, 3848, 7921, 8312, 4720, 1472, 256, 1, 82, 1369, 8254, 22841, 33002, 26704, 12448, 3328, 512

Offset: 0

Author

Peter Luschny, Feb 10 2018

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 1,  2
[2] 1,  5,    4
[3] 1, 10,   16,    8
[4] 1, 17,   49,   44,   16
[5] 1, 26,  121,  182,  112,     32
[6] 1, 37,  256,  593,  584,    272,    64
[7] 1, 50,  484, 1616, 2368,   1712,   640,   128
[8] 1, 65,  841, 3848, 7921,   8312,  4720,  1472,  256
[9] 1, 82, 1369, 8254, 22841, 33002, 26704, 12448, 3328, 512
		

Crossrefs

Cf. A299443 (row sums).

Programs

Maple

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