Triangle read by rows: T(n,k) = Sum_{i=n-k..n} C(k-1,n-i)*C(i,n-k)*C(2*i,i)/(i+1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =3a(6) =5a(7) =15a(8) =19a(9) =10a(10) =14a(11) =56a(12) =99a(13) =90a(14) =36a(15) =42a(16) =210a(17) =476a(18) =603a(19) =427a(20) =137a(21) =132a(22) =792a(23) =2190a(24) =3536a(25) =3507a(26) =2032a(27) =543a(28) =429a(29) =3003