Triangle read by rows, T(n,k) = k^(n-k)*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =0a(5) =1a(6) =0a(7) =1a(8) =0a(9) =1a(10) =0a(11) =2a(12) =4a(13) =0a(14) =1a(15) =0a(16) =9a(17) =16a(18) =9a(19) =0a(20) =1a(21) =0a(22) =44a(23) =144a(24) =54a(25) =16a(26) =0a(27) =1a(28) =0a(29) =265