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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =7a(5) =1a(6) =1a(7) =19a(8) =19a(9) =1a(10) =1a(11) =39a(12) =171a(13) =39a(14) =1a(15) =1a(16) =69a(17) =761a(18) =761a(19) =69a(20) =1a(21) =1a(22) =111a(23) =2429a(24) =8533a(25) =2429a(26) =111a(27) =1a(28) =1a(29) =167