A272867 Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-2) where m = k if k<n else 2*n-k, for n>=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

0,3

Links

Indranil Ghosh, Rows 0..50, flattened

Formula

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

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

Example

                                  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;

Maple

T := (n, k) -> simplify(GegenbauerC(`if`(k<n, k, 2*n-k), -n, -2)):
for n from 0 to 8 do seq(T(n, k), k=0..2*n) od;

Mathematica

T[n_, k_]:=If[n<1, 1, If[k<n, GegenbauerC[k, -n, -2], GegenbauerC[2n - k, -n, -2]]]; Table[T[n, k], {n, 0, 10}, {k, 0, 2n}] // Flatten (* Indranil Ghosh, Apr 03 2017 *)

Crossrefs

Cf. A005572, A081671.

Sequence in context: A317703 A055107 A297193 * A206438 A331148 A128137

Adjacent sequences: A272864 A272865 A272866 * A272868 A272869 A272870

Keyword

nonn,tabf

Author

Peter Luschny, May 08 2016

Status

approved