Triangle T(n,k) = A000142(n-k)*A003319(k+1) read by rows.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =1a(5) =3a(6) =6a(7) =2a(8) =3a(9) =13a(10) =24a(11) =6a(12) =6a(13) =13a(14) =71a(15) =120a(16) =24a(17) =18a(18) =26a(19) =71a(20) =461a(21) =720a(22) =120a(23) =72a(24) =78a(25) =142a(26) =461a(27) =3447a(28) =5040a(29) =720