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

Terms

a(0) =1a(1) =3a(2) =1a(3) =10a(4) =7a(5) =1a(6) =35a(7) =31a(8) =13a(9) =1a(10) =126a(11) =121a(12) =81a(13) =21a(14) =1a(15) =462a(16) =456a(17) =381a(18) =181a(19) =31a(20) =1a(21) =1716a(22) =1709a(23) =1583a(24) =1058a(25) =358a(26) =43a(27) =1a(28) =6435a(29) =6427