Square array where T(n,k) = Sum_{j=0..k} C(n+2*j,j)*C(n+2*j,k-j), read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =4a(5) =10a(6) =1a(7) =6a(8) =19a(9) =46a(10) =1a(11) =8a(12) =32a(13) =94a(14) =226a(15) =1a(16) =10a(17) =49a(18) =170a(19) =474a(20) =1136a(21) =1a(22) =12a(23) =70a(24) =282a(25) =899a(26) =2431a(27) =5810a(28) =1a(29) =14