Square array T(n, k) = Product_{j=1..n} A129862(k+1, j) with T(n, 0) = n!, read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =1a(7) =1a(8) =0a(9) =6a(10) =1a(11) =1a(12) =-1a(13) =0a(14) =24a(15) =1a(16) =1a(17) =-2a(18) =-1a(19) =0a(20) =120a(21) =1a(22) =1a(23) =-3a(24) =-8a(25) =-1a(26) =0a(27) =720a(28) =1a(29) =1