Square array read by antidiagonals with T(n,k)=T(n,k-1)^2+n*T(n,k-1)+1 and T(n,0)=0.

Terms

a(0) =0a(1) =1a(2) =0a(3) =2a(4) =1a(5) =0a(6) =5a(7) =3a(8) =1a(9) =0a(10) =26a(11) =13a(12) =4a(13) =1a(14) =0a(15) =677a(16) =183a(17) =25a(18) =5a(19) =1a(20) =0a(21) =458330a(22) =33673a(23) =676a(24) =41a(25) =6a(26) =1a(27) =0a(28) =210066388901a(29) =1133904603