A376827 T(n, k) = binomial(n, k)*hypergeom([(1 - n)/2, -n/2], [1], 4).

1, 1, 1, 3, 6, 3, 7, 21, 21, 7, 19, 76, 114, 76, 19, 51, 255, 510, 510, 255, 51, 141, 846, 2115, 2820, 2115, 846, 141, 393, 2751, 8253, 13755, 13755, 8253, 2751, 393, 1107, 8856, 30996, 61992, 77490, 61992, 30996, 8856, 1107

Offset: 0

Author

Peter Luschny, Oct 05 2024

Keywords

• nonn
• tabl

Examples

			[0]    1;
[1]    1,    1;
[2]    3,    6,     3;
[3]    7,   21,    21,     7;
[4]   19,   76,   114,    76,    19;
[5]   51,  255,   510,   510,   255,    51;
[6]  141,  846,  2115,  2820,  2115,   846,   141;
[7]  393, 2751,  8253, 13755, 13755,  8253,  2751,  393;
[8] 1107, 8856, 30996, 61992, 77490, 61992, 30996, 8856, 1107;
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).

Crossrefs

Cf. A002426 (column 0 and main diagonal), A098453 (row sums).

Programs

Maple

T := (n, k) -> binomial(n, k)*hypergeom([(1 - n)/2, -n/2], [1], 4): seq(seq(simplify(T(n, k)), k = 0..n), n = 0..8);

Mathematica

A376827[n_, k_] := Binomial[n, k]*Hypergeometric2F1[(1-n)/2, -n/2, 1, 4];
Table[A376827[n, k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Oct 21 2024 *)

Formula

T(n, k) = binomial(n, k)* A002426(n). - Detlef Meya, Oct 11 2024