Triangle read by rows: T(n, k) = (n + 1) * Sum_{j=k..n} binomial(n, j) * Eulerian1(j, j - k).

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =9a(5) =3a(6) =4a(7) =28a(8) =28a(9) =4a(10) =5a(11) =75a(12) =165a(13) =75a(14) =5a(15) =6a(16) =186a(17) =786a(18) =786a(19) =186a(20) =6a(21) =7a(22) =441a(23) =3311a(24) =6181a(25) =3311a(26) =441a(27) =7a(28) =8a(29) =1016