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

%I A272868 #9 May 08 2016 10:11:11
%S A272868 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,
%T A272868 1206,2841,1,7,49,203,791,2261,6027,12489,1,8,60,280,1190,3864,11452,
%U A272868 27560,60705,1,9,72,372,1710,6174,20076,54468,134073,281185
%N A272868 Triangle read by rows, T(n,k) = 2^k*GegenbauerC(k,-n,-1/4), for n>=0 and 0<=k<=n.
%F A272868 T(n,n) = A084605(n).
%F A272868 T(n,n-1) = A098520(n).
%F A272868 T(n+1,n)/(n+1) = A091147(n).
%e A272868 Triangle starts:
%e A272868                                 1;
%e A272868                               1, 1;
%e A272868                             1, 2, 9;
%e A272868                           1, 3, 15, 25;
%e A272868                        1, 4, 22, 52, 145;
%e A272868                      1, 5, 30, 90, 285, 561;
%e A272868                  1, 6, 39, 140, 495, 1206, 2841;
%e A272868              1, 7, 49, 203, 791, 2261, 6027, 12489;
%p A272868 T := (n,k) -> simplify(2^k*GegenbauerC(k, -n, -1/4)):
%p A272868 for n from 0 to 9 do seq(T(n,k), k=0..n) od;
%t A272868 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 *)
%Y A272868 Cf. A084605, A091147, A098520.
%K A272868 nonn,tabl
%O A272868 0,5
%A A272868 _Peter Luschny_, May 08 2016