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

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =5a(6) =1a(7) =4a(8) =10a(9) =16a(10) =1a(11) =5a(12) =17a(13) =41a(14) =65a(15) =1a(16) =6a(17) =26a(18) =86a(19) =206a(20) =326a(21) =1a(22) =7a(23) =37a(24) =157a(25) =517a(26) =1237a(27) =1957a(28) =1a(29) =8