Generalized Bell numbers based on the rising factorial powers; square array read by antidiagonals.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =2a(8) =3a(9) =1a(10) =1a(11) =5a(12) =27a(13) =13a(14) =1a(15) =1a(16) =15a(17) =409a(18) =778a(19) =73a(20) =1a(21) =1a(22) =52a(23) =9089a(24) =104149a(25) =37553a(26) =501a(27) =1a(28) =1a(29) =203