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

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =7a(5) =5a(6) =1a(7) =15a(8) =32a(9) =13a(10) =1a(11) =26a(12) =111a(13) =123a(14) =34a(15) =1a(16) =40a(17) =285a(18) =603a(19) =429a(20) =89a(21) =1a(22) =57a(23) =610a(24) =2094a(25) =2748a(26) =1408a(27) =233a(28) =1a(29) =77