Array read by antidiagonals of higher order Bell numbers.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =3a(5) =5a(6) =1a(7) =4a(8) =12a(9) =15a(10) =1a(11) =5a(12) =22a(13) =60a(14) =52a(15) =1a(16) =6a(17) =35a(18) =154a(19) =358a(20) =203a(21) =1a(22) =7a(23) =51a(24) =315a(25) =1304a(26) =2471a(27) =877a(28) =1a(29) =8