Square array A(n,k) = (n!)^3 [x^n] hypergeom([], [1, 1], z)^k read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =0a(3) =1a(4) =1a(5) =0a(6) =1a(7) =2a(8) =1a(9) =0a(10) =1a(11) =3a(12) =10a(13) =1a(14) =0a(15) =1a(16) =4a(17) =27a(18) =56a(19) =1a(20) =0a(21) =1a(22) =5a(23) =52a(24) =381a(25) =346a(26) =1a(27) =0a(28) =1a(29) =6