Triangle T[n,m]: T[n,-1] = 0; T[0,0] = 0; T[n,0] = n*n!; T[n,m] = T[n,m-1] - T[n-1,m-1].

Terms

a(0) =0a(1) =1a(2) =1a(3) =4a(4) =3a(5) =2a(6) =18a(7) =14a(8) =11a(9) =9a(10) =96a(11) =78a(12) =64a(13) =53a(14) =44a(15) =600a(16) =504a(17) =426a(18) =362a(19) =309a(20) =265a(21) =4320a(22) =3720a(23) =3216a(24) =2790a(25) =2428a(26) =2119a(27) =1854a(28) =35280a(29) =30960