Array read by rows: T(n,k) = binomial(n+k-2,k-1)*binomial(2*n-1,n-k).

Terms

a(0) =1a(1) =3a(2) =2a(3) =10a(4) =15a(5) =6a(6) =35a(7) =84a(8) =70a(9) =20a(10) =126a(11) =420a(12) =540a(13) =315a(14) =70a(15) =462a(16) =1980a(17) =3465a(18) =3080a(19) =1386a(20) =252a(21) =1716a(22) =9009a(23) =20020a(24) =24024a(25) =16380a(26) =6006a(27) =924a(28) =6435a(29) =40040