Triangle, read by rows, where T(n,k) = binomial(n*(n-1)/2 - k*(k-1)/2 + n-k+3, n-k).

Terms

a(0) =1a(1) =4a(2) =1a(3) =15a(4) =5a(5) =1a(6) =84a(7) =28a(8) =6a(9) =1a(10) =715a(11) =220a(12) =45a(13) =7a(14) =1a(15) =8568a(16) =2380a(17) =455a(18) =66a(19) =8a(20) =1a(21) =134596a(22) =33649a(23) =5985a(24) =816a(25) =91a(26) =9a(27) =1a(28) =2629575a(29) =593775