Triangle read by rows, T(n, k) = [x^k] (1-x)^(n+1)*Sum_{j=0..n} binomial(n + n*j + j, n*j + j)*x^j.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =7a(5) =1a(6) =1a(7) =31a(8) =31a(9) =1a(10) =1a(11) =121a(12) =381a(13) =121a(14) =1a(15) =1a(16) =456a(17) =3431a(18) =3431a(19) =456a(20) =1a(21) =1a(22) =1709a(23) =26769a(24) =60691a(25) =26769a(26) =1709a(27) =1a(28) =1a(29) =6427