Triangle T(n,k)=Sum_{i=0..n} |stirling1(n,n-i)|*binomial(i,k), k=0..n-1.

Terms

a(0) =1a(1) =2a(2) =1a(3) =6a(4) =7a(5) =2a(6) =24a(7) =46a(8) =29a(9) =6a(10) =120a(11) =326a(12) =329a(13) =146a(14) =24a(15) =720a(16) =2556a(17) =3604a(18) =2521a(19) =874a(20) =120a(21) =5040a(22) =22212a(23) =40564a(24) =39271a(25) =21244a(26) =6084a(27) =720a(28) =40320a(29) =212976