Triangle read by rows: T(n,k) = (4k+3)/(n+2k+2)*binomial(2n,n+2k+1).

Terms

a(0) =0a(1) =1a(2) =3a(3) =9a(4) =1a(5) =28a(6) =7a(7) =90a(8) =35a(9) =1a(10) =297a(11) =154a(12) =11a(13) =1001a(14) =637a(15) =77a(16) =1a(17) =3432a(18) =2548a(19) =440a(20) =15a(21) =11934a(22) =9996a(23) =2244a(24) =135a(25) =1a(26) =41990a(27) =38760a(28) =10659a(29) =950