Triangle T(n,k) = Sum_{j=0..k} Stirling1(n, n-j)*binomial(n,j), read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =-1a(5) =-1a(6) =1a(7) =-8a(8) =-2a(9) =-2a(10) =1a(11) =-23a(12) =43a(13) =19a(14) =19a(15) =1a(16) =-49a(17) =301a(18) =-199a(19) =-79a(20) =-79a(21) =1a(22) =-89a(23) =1186a(24) =-3314a(25) =796a(26) =76a(27) =76a(28) =1a(29) =-146