Triangle T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!), read by rows.

Terms

a(0) =1a(1) =3a(2) =4a(3) =11a(4) =28a(5) =24a(6) =42a(7) =156a(8) =225a(9) =160a(10) =163a(11) =792a(12) =1596a(13) =1736a(14) =1120a(15) =638a(16) =3820a(17) =9855a(18) =14400a(19) =13230a(20) =8064a(21) =2510a(22) =17832a(23) =55968a(24) =102520a(25) =122265a(26) =100584a(27) =59136a(28) =9908a(29) =81368