A272868 Triangle read by rows, T(n,k) = 2^k*GegenbauerC(k,-n,-1/4), for n>=0 and 0<=k<=n.

1, 1, 1, 1, 2, 9, 1, 3, 15, 25, 1, 4, 22, 52, 145, 1, 5, 30, 90, 285, 561, 1, 6, 39, 140, 495, 1206, 2841, 1, 7, 49, 203, 791, 2261, 6027, 12489, 1, 8, 60, 280, 1190, 3864, 11452, 27560, 60705, 1, 9, 72, 372, 1710, 6174, 20076, 54468, 134073, 281185

Offset: 0

Author

Peter Luschny, May 08 2016

Keywords

• nonn
• tabl

Examples

			Triangle starts:
                                1;
                              1, 1;
                            1, 2, 9;
                          1, 3, 15, 25;
                       1, 4, 22, 52, 145;
                     1, 5, 30, 90, 285, 561;
                 1, 6, 39, 140, 495, 1206, 2841;
             1, 7, 49, 203, 791, 2261, 6027, 12489;
		

Crossrefs

Cf. A084605, A091147, A098520.

Programs

Maple

T := (n,k) -> simplify(2^k*GegenbauerC(k, -n, -1/4)):
for n from 0 to 9 do seq(T(n,k), k=0..n) od;

Mathematica

Table[If[n == 0, 1, 2^k GegenbauerC[k, -n, -1/4]], {n, 0, 9}, {k, 0, n}] // Flatten (* Michael De Vlieger, May 08 2016 *)

Formula

T(n,n) = A084605(n).

T(n,n-1) = A098520(n).

T(n+1,n)/(n+1) = A091147(n).