A243163 - OEIS

%I #6 Jan 22 2022 16:48:32

%S 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 1428,0,0,0,0,455,4760,11628,7752,0,0,0,0,140,6120,38760,74613,43263,

%U 0,0,0,0,0,3876,67830,302841,480700,246675,0,0,0,0,0,969,65835

%N 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 T(n, n) = A001764(n).

%F T(2*n,n) = A002293(n).

%F Sum_{k=0..n} T(n, k) = A186997(n).

%e                                1;

%e                               0, 1;

%e                             0, 1, 3;

%e                           0, 0, 7, 12;

%e                         0, 0, 4, 45, 55;

%e                      0, 0, 0, 55, 286, 273;

%p T := (n, k) -> binomial(k,n-k)*binomial(n+2*k,n+k)/(n+k+1);

%p seq(print(seq(T(n,k), k=0..n)), n=0..10);

%Y Cf. A001764, A002293, A186997.

%K nonn,tabl

%O 0,6

%A _Peter Luschny_, May 31 2014