A320904 T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.

1, 1, 3, 1, 5, 7, 1, 7, 16, 15, 1, 9, 29, 42, 31, 1, 11, 46, 93, 99, 63, 1, 13, 67, 176, 256, 219, 127, 1, 15, 92, 299, 562, 638, 466, 255, 1, 17, 121, 470, 1093, 1586, 1486, 968, 511, 1, 19, 154, 697, 1941, 3473, 4096, 3302, 1981, 1023

Offset: 0

Author

Peter Luschny, Oct 28 2018

Keywords

• nonn
• tabl

Examples

			Triangle starts:
[0] 1
[1] 1,  3
[2] 1,  5,   7
[3] 1,  7,  16,  15
[4] 1,  9,  29,  42,   31
[5] 1, 11,  46,  93,   99,   63
[6] 1, 13,  67, 176,  256,  219,  127
[7] 1, 15,  92, 299,  562,  638,  466, 255
[8] 1, 17, 121, 470, 1093, 1586, 1486, 968, 511
		

Crossrefs

Row sums are A105693(n-1).

Cf. A097750.

Programs

Maple

T := (n, k) -> binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n-k+1)], -1):
for n from 0 to 11 do seq(simplify(T(n, k)), k = 0..n) od;

Mathematica

s={};For[n=0,n<19,n++,For[k=0,kDetlef Meya, Oct 03 2023 *)