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

Terms

a(0) =1a(1) =3a(2) =1a(3) =20a(4) =15a(5) =1a(6) =175a(7) =189a(8) =35a(9) =1a(10) =1764a(11) =2352a(12) =720a(13) =63a(14) =1a(15) =19404a(16) =29700a(17) =12375a(18) =1925a(19) =99a(20) =1a(21) =226512a(22) =382239a(23) =196625a(24) =44044a(25) =4212a(26) =143a(27) =1a(28) =2760615a(29) =5010005