Floor-Sqrt transform of ordered Bell numbers (A000670).

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =8a(5) =23a(6) =68a(7) =217a(8) =738a(9) =2662a(10) =10111a(11) =40281a(12) =167605a(13) =725850a(14) =3262107a(15) =15175084a(16) =72908536a(17) =361068922a(18) =1839982245a(19) =9633358049a(20) =51746379547a(21) =284824200163