OFFSET
0,5
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
EXAMPLE
[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, ...
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Mar 16 2018
STATUS
approved