Triangle, read by rows, T(n,k) = binomial(n*(n-k)*k, k) + binomial(n*(n-k)*k, n -k).

Terms

a(0) =2a(1) =1a(2) =1a(3) =1a(4) =4a(5) =1a(6) =1a(7) =21a(8) =21a(9) =1a(10) =1a(11) =232a(12) =240a(13) =232a(14) =1a(15) =1a(16) =4865a(17) =4495a(18) =4495a(19) =4865a(20) =1a(21) =1a(22) =142536a(23) =195708a(24) =49608a(25) =195708a(26) =142536a(27) =1a(28) =1a(29) =5245828