Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 1, n-k) for n>=k>=0.

Terms

a(0) =1a(1) =2a(2) =1a(3) =10a(4) =4a(5) =1a(6) =165a(7) =45a(8) =7a(9) =1a(10) =5985a(11) =1140a(12) =136a(13) =11a(14) =1a(15) =376992a(16) =52360a(17) =4960a(18) =325a(19) =16a(20) =1a(21) =36288252a(22) =3819816a(23) =292825a(24) =16215a(25) =666a(26) =22a(27) =1a(28) =4935847320a(29) =406481544