Triangle of numbers T(n,k) = (-1)^(n-k)*(n+1)!*Stirling2(n,k)/(k+1).

Terms

a(0) =1a(1) =-3a(2) =2a(3) =12a(4) =-24a(5) =6a(6) =-60a(7) =280a(8) =-180a(9) =24a(10) =360a(11) =-3600a(12) =4500a(13) =-1440a(14) =120a(15) =-2520a(16) =52080a(17) =-113400a(18) =65520a(19) =-12600a(20) =720a(21) =20160a(22) =-846720a(23) =3034080a(24) =-2822400a(25) =940800a(26) =-120960a(27) =5040a(28) =-181440a(29) =15361920