A recursion triangle sequence based on the Eulerian numbers: A(n,k)=n*A(n-1,k-1)+k*Eulerian(n-1,k).

Terms

a(0) =1a(1) =2a(2) =1a(3) =7a(4) =6a(5) =1a(6) =28a(7) =30a(8) =24a(9) =1a(10) =131a(11) =162a(12) =153a(13) =120a(14) =1a(15) =746a(16) =918a(17) =1050a(18) =922a(19) =720a(20) =1a(21) =5097a(22) =5826a(23) =7332a(24) =7578a(25) =6459a(26) =5040a(27) =1a(28) =40440a(29) =43158