A301477 T(n,k) = Sum_{j=0..n-k} H(n,j)*2^k with H(n,k) = binomial(n,k)* hypergeom([-k/2, 1/2-k/2], [2-k+n], 4), for 0 <= k <= n, triangle read by rows.

1, 2, 2, 5, 6, 4, 13, 18, 16, 8, 35, 52, 56, 40, 16, 96, 150, 180, 160, 96, 32, 267, 432, 560, 568, 432, 224, 64, 750, 1246, 1708, 1904, 1680, 1120, 512, 128, 2123, 3600, 5152, 6160, 6048, 4736, 2816, 1152, 256, 6046, 10422, 15432, 19488, 20736, 18240, 12864, 6912, 2560, 512

Offset

0,2

Links

Table of n, a(n) for n=0..54.

Example

                               1
                              2, 2
                            5, 6, 4
                         13, 18, 16, 8
                       35, 52, 56, 40, 16
                   96, 150, 180, 160, 96, 32
                267, 432, 560, 568, 432, 224, 64
          750, 1246, 1708, 1904, 1680, 1120, 512, 128
      2123, 3600, 5152, 6160, 6048, 4736, 2816, 1152, 256

Maple

H := (n, k) -> binomial(n, k)*hypergeom([-k/2, 1/2-k/2], [2-k+n], 4):
T := (n, k) -> add(simplify(H(n, j)*2^k), j=0..n-k):
seq(seq(T(n, k), k=0..n), n=0..9);

Mathematica

s={}; For[n=0, n<13, n++, For[k=0, k<n+1, k++, AppendTo[s, (2^k)*(GegenbauerC[n-k-1, -n, -1/2]+GegenbauerC[n-k, -n, -1/2]+KroneckerDelta[n])]]]; s (* Detlef Meya, Oct 03 2023 *)

Crossrefs

Row sums are A126932, first column A005773, diagonal A000079.

Cf. A301475 (general case).

Sequence in context: A367211 A250303 A368554 * A261895 A112573 A233740

Adjacent sequences: A301474 A301475 A301476 * A301478 A301479 A301480

Keyword

nonn,tabl

Author

Peter Luschny, Mar 22 2018

Status

approved