A272867 Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-2) where m = k if k=0 and 0<=k<=2n.

1, 1, 4, 1, 1, 8, 18, 8, 1, 1, 12, 51, 88, 51, 12, 1, 1, 16, 100, 304, 454, 304, 100, 16, 1, 1, 20, 165, 720, 1770, 2424, 1770, 720, 165, 20, 1, 1, 24, 246, 1400, 4815, 10224, 13236, 10224, 4815, 1400, 246, 24, 1

Offset: 0

Author

Peter Luschny, May 08 2016

Keywords

• nonn
• tabf

Examples

			                                  1;
                            1,    4,  1;
                         1, 8,   18,  8, 1;
                    1, 12, 51,   88,  51, 12, 1;
              1, 16, 100, 304,  454,  304, 100, 16, 1;
        1, 20, 165, 720, 1770, 2424,  1770, 720, 165, 20, 1;
1, 24, 246, 1400, 4815, 10224, 13236, 10224, 4815, 1400, 246, 24, 1;
		

Links

• Indranil Ghosh, Rows 0..50, flattened

Crossrefs

Cf. A005572, A081671.

Programs

Maple

T := (n,k) -> simplify(GegenbauerC(`if`(k
				

Mathematica

T[n_, k_]:=If[n<1, 1, If[kIndranil Ghosh, Apr 03 2017 *)

Formula

T(n,n) = A081671(n) for n>=0.

T(n+1,n+2)/(n+1) = A005572(n) for n>=0.