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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.

%I A301477 #18 Oct 04 2023 04:48:57
%S A301477 1,2,2,5,6,4,13,18,16,8,35,52,56,40,16,96,150,180,160,96,32,267,432,
%T A301477 560,568,432,224,64,750,1246,1708,1904,1680,1120,512,128,2123,3600,
%U A301477 5152,6160,6048,4736,2816,1152,256,6046,10422,15432,19488,20736,18240,12864,6912,2560,512
%N 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.
%e A301477                                1
%e A301477                               2, 2
%e A301477                             5, 6, 4
%e A301477                          13, 18, 16, 8
%e A301477                        35, 52, 56, 40, 16
%e A301477                    96, 150, 180, 160, 96, 32
%e A301477                 267, 432, 560, 568, 432, 224, 64
%e A301477           750, 1246, 1708, 1904, 1680, 1120, 512, 128
%e A301477       2123, 3600, 5152, 6160, 6048, 4736, 2816, 1152, 256
%p A301477 H := (n,k) -> binomial(n,k)*hypergeom([-k/2,1/2-k/2],[2-k+n], 4):
%p A301477 T := (n,k) -> add(simplify(H(n,j)*2^k), j=0..n-k):
%p A301477 seq(seq(T(n,k), k=0..n), n=0..9);
%t A301477 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 *)
%Y A301477 Row sums are A126932, first column A005773, diagonal A000079.
%Y A301477 Cf. A301475 (general case).
%K A301477 nonn,tabl
%O A301477 0,2
%A A301477 _Peter Luschny_, Mar 22 2018