Triangle read by rows: T(n,k) = (Sum_{i=k..n} i!)/(k!) for 0 <= k <= n.

Terms

a(0) =1a(1) =2a(2) =1a(3) =4a(4) =3a(5) =1a(6) =10a(7) =9a(8) =4a(9) =1a(10) =34a(11) =33a(12) =16a(13) =5a(14) =1a(15) =154a(16) =153a(17) =76a(18) =25a(19) =6a(20) =1a(21) =874a(22) =873a(23) =436a(24) =145a(25) =36a(26) =7a(27) =1a(28) =5914a(29) =5913