Triangle read by rows: T(n, k) = n^k * Sum_{j=0..n} binomial(n - j, n - k) * Eulerian1(n, j).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =6a(5) =8a(6) =1a(7) =21a(8) =108a(9) =162a(10) =1a(11) =60a(12) =800a(13) =3840a(14) =6144a(15) =1a(16) =155a(17) =4500a(18) =48750a(19) =225000a(20) =375000a(21) =1a(22) =378a(23) =21672a(24) =453600a(25) =4354560a(26) =19595520a(27) =33592320a(28) =1a(29) =889