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A243163 Triangle read by rows: T(n,k) = binomial(k,n-k)*binomial(n+2*k,n+k) /(n+k+1), n>=0, 0<=k<=n.

%I A243163 #6 Jan 22 2022 16:48:32
%S A243163 1,0,1,0,1,3,0,0,7,12,0,0,4,45,55,0,0,0,55,286,273,0,0,0,22,546,1820,
%T A243163 1428,0,0,0,0,455,4760,11628,7752,0,0,0,0,140,6120,38760,74613,43263,
%U A243163 0,0,0,0,0,3876,67830,302841,480700,246675,0,0,0,0,0,969,65835
%N A243163 Triangle read by rows: T(n,k) = binomial(k,n-k)*binomial(n+2*k,n+k) /(n+k+1), n>=0, 0<=k<=n.
%F A243163 T(n, n) = A001764(n).
%F A243163 T(2*n,n) = A002293(n).
%F A243163 Sum_{k=0..n} T(n, k) = A186997(n).
%e A243163                                1;
%e A243163                               0, 1;
%e A243163                             0, 1, 3;
%e A243163                           0, 0, 7, 12;
%e A243163                         0, 0, 4, 45, 55;
%e A243163                      0, 0, 0, 55, 286, 273;
%p A243163 T := (n, k) -> binomial(k,n-k)*binomial(n+2*k,n+k)/(n+k+1);
%p A243163 seq(print(seq(T(n,k), k=0..n)), n=0..10);
%Y A243163 Cf. A001764, A002293, A186997.
%K A243163 nonn,tabl
%O A243163 0,6
%A A243163 _Peter Luschny_, May 31 2014