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

%I A272867 #9 Apr 03 2017 20:37:57
%S A272867 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,
%T A272867 1,20,165,720,1770,2424,1770,720,165,20,1,1,24,246,1400,4815,10224,
%U A272867 13236,10224,4815,1400,246,24,1
%N 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.
%H A272867 Indranil Ghosh, <a href="/A272867/b272867.txt">Rows 0..50, flattened</a>
%F A272867 T(n,n) = A081671(n) for n>=0.
%F A272867 T(n+1,n+2)/(n+1) = A005572(n) for n>=0.
%e A272867                                   1;
%e A272867                             1,    4,  1;
%e A272867                          1, 8,   18,  8, 1;
%e A272867                     1, 12, 51,   88,  51, 12, 1;
%e A272867               1, 16, 100, 304,  454,  304, 100, 16, 1;
%e A272867         1, 20, 165, 720, 1770, 2424,  1770, 720, 165, 20, 1;
%e A272867 1, 24, 246, 1400, 4815, 10224, 13236, 10224, 4815, 1400, 246, 24, 1;
%p A272867 T := (n,k) -> simplify(GegenbauerC(`if`(k<n,k,2*n-k),-n, -2)):
%p A272867 for n from 0 to 8 do seq(T(n,k), k=0..2*n) od;
%t A272867 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 *)
%Y A272867 Cf. A005572, A081671.
%K A272867 nonn,tabf
%O A272867 0,3
%A A272867 _Peter Luschny_, May 08 2016