Table by antidiagonals of T(n,k) = n*T(n,k-1) + T(n,k-2) starting with T(n,1) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =2a(6) =1a(7) =3a(8) =5a(9) =3a(10) =1a(11) =4a(12) =10a(13) =12a(14) =5a(15) =1a(16) =5a(17) =17a(18) =33a(19) =29a(20) =8a(21) =1a(22) =6a(23) =26a(24) =72a(25) =109a(26) =70a(27) =13a(28) =1a(29) =7