A300945 Rectangular array A(n, k) = hypergeom([-k, k + n/2 - 1], [1], -4) with row n >= 0 and k >= 0, read by ascending antidiagonals.

1, 1, 1, 1, 3, 25, 1, 5, 43, 425, 1, 7, 65, 661, 7025, 1, 9, 91, 965, 10515, 116625, 1, 11, 121, 1345, 15105, 171097, 1951625, 1, 13, 155, 1809, 20995, 243525, 2828101, 32903225, 1, 15, 193, 2365, 28401, 337877, 4001345, 47284251, 558265825

Offset: 0

Author

Peter Luschny, Mar 16 2018

Keywords

• nonn
• tabl

Examples

			[0] 1,  1,  25,  425,  7025, 116625,  1951625,  32903225, ... [A299845]
[1] 1,  3,  43,  661, 10515, 171097,  2828101,  47284251, ... [A299506]
[2] 1,  5,  65,  965, 15105, 243525,  4001345,  66622085, ...
[3] 1,  7,  91, 1345, 20995, 337877,  5544709,  92234527, ... [A243946]
[4] 1,  9, 121, 1809, 28401, 458649,  7544041, 125700129, ... [A084769]
[5] 1, 11, 155, 2365, 37555, 610897, 10098997, 168894355, ... [A243947]
[6] 1, 13, 193, 3021, 48705, 800269, 13324417, 224028877, ...
		

Crossrefs

Cf. A299845, A299506, A243946, A084769, A243947.

Cf. A300946.

Programs

Mathematica

Arow[n_, len_] := Table[Hypergeometric2F1[-k, k + n/2 - 1, 1, -4], {k, 0, len}];
Table[Print[Arow[n, 7]], {n, 0, 6}];
T[n_, k_] := If[k==0, 1, 4^k*Sum[(5/4)^j*Binomial[k, j]*Binomial[k - 2 + ((n - k)/2), j - 2 + ((n - k)/2)] ,{j, 0, n}]]; Flatten[Table[T[n, k],{n, 0, 8}, {k, 0, n}]] (* Detlef Meya, May 28 2024 *)

Formula

T(n, k) = if k = 0 then 1, otherwise 4^k*Sum_{j=0..n} (5/4)^j * binomial(k, j) * binomial(k - 2 + ((n - k)/2), j - 2 + ((n - k)/2)). - Detlef Meya, May 28 2024