Triangle T(n, k) = Sum_{j=0..k-1} (-1)^j*binomial(k, j+1)*(k-j)^(n-k), read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =1a(6) =1a(7) =7a(8) =4a(9) =1a(10) =1a(11) =15a(12) =16a(13) =5a(14) =1a(15) =1a(16) =31a(17) =58a(18) =25a(19) =6a(20) =1a(21) =1a(22) =63a(23) =196a(24) =125a(25) =36a(26) =7a(27) =1a(28) =1a(29) =127