Triangle read by rows: T(n, k) = Sum_{j=0..n} j! * binomial(n - j, n - k).

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =4a(6) =1a(7) =4a(8) =7a(9) =10a(10) =1a(11) =5a(12) =11a(13) =17a(14) =34a(15) =1a(16) =6a(17) =16a(18) =28a(19) =51a(20) =154a(21) =1a(22) =7a(23) =22a(24) =44a(25) =79a(26) =205a(27) =874a(28) =1a(29) =8