T(n, k) = [x^k] Sum_{j=0..n} j!*binomial(x, j), for 0 <= k <= n, triangle read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =0a(5) =1a(6) =1a(7) =2a(8) =-2a(9) =1a(10) =1a(11) =-4a(12) =9a(13) =-5a(14) =1a(15) =1a(16) =20a(17) =-41a(18) =30a(19) =-9a(20) =1a(21) =1a(22) =-100a(23) =233a(24) =-195a(25) =76a(26) =-14a(27) =1a(28) =1a(29) =620