Triangle, read by rows: T(0,0) = 1; T(n,k) = n!*T(n-1,k) - T(n-1,k-1).

Terms

a(0) =1a(1) =1a(2) =-1a(3) =2a(4) =-3a(5) =1a(6) =12a(7) =-20a(8) =9a(9) =-1a(10) =288a(11) =-492a(12) =236a(13) =-33a(14) =1a(15) =34560a(16) =-59328a(17) =28812a(18) =-4196a(19) =153a(20) =-1a(21) =24883200a(22) =-42750720a(23) =20803968a(24) =-3049932a(25) =114356a(26) =-873a(27) =1a(28) =125411328000a(29) =-215488512000