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

Terms

a(0) =1a(1) =-6a(2) =-6a(3) =36a(4) =64a(5) =36a(6) =-240a(7) =-600a(8) =-600a(9) =-240a(10) =1800a(11) =5760a(12) =8100a(13) =5760a(14) =1800a(15) =-15120a(16) =-58800a(17) =-105840a(18) =-105840a(19) =-58800a(20) =-15120a(21) =141120a(22) =645120a(23) =1411200a(24) =1806336a(25) =1411200a(26) =645120a(27) =141120a(28) =-1451520a(29) =-7620480