Triangle read by rows: T(n,k) = Sum_{j=k..n} binomial(n + j, n)*binomial(n, j)/(j + 1).

Terms

a(0) =1a(1) =2a(2) =1a(3) =6a(4) =5a(5) =2a(6) =22a(7) =21a(8) =15a(9) =5a(10) =90a(11) =89a(12) =79a(13) =49a(14) =14a(15) =394a(16) =393a(17) =378a(18) =308a(19) =168a(20) =42a(21) =1806a(22) =1805a(23) =1784a(24) =1644a(25) =1224a(26) =594a(27) =132a(28) =8558a(29) =8557