A triangle sequence of the form:q=3:t(n,m,q)=Sum[q^i*Floor[Eulerian[n + 1, m]/2^i], {i, 0, 10}].

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =19a(5) =1a(6) =1a(7) =71a(8) =71a(9) =1a(10) =1a(11) =281a(12) =2064a(13) =281a(14) =1a(15) =1a(16) =942a(17) =19925a(18) =19925a(19) =942a(20) =1a(21) =1a(22) =3000a(23) =182094a(24) =372304a(25) =182094a(26) =3000a(27) =1a(28) =1a(29) =9265