Triangle read by rows: T(k,j) = ((2*j+1)/(k+1))*binomial(2*j,j)*binomial(2*k-2*j,k-j).

Terms

a(0) =1a(1) =1a(2) =3a(3) =2a(4) =4a(5) =10a(6) =5a(7) =9a(8) =15a(9) =35a(10) =14a(11) =24a(12) =36a(13) =56a(14) =126a(15) =42a(16) =70a(17) =100a(18) =140a(19) =210a(20) =462a(21) =132a(22) =216a(23) =300a(24) =400a(25) =540a(26) =792a(27) =1716a(28) =429a(29) =693