a(n) = ceiling(sqrt(n!)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =11a(6) =27a(7) =71a(8) =201a(9) =603a(10) =1905a(11) =6318a(12) =21887a(13) =78912a(14) =295260a(15) =1143536a(16) =4574144a(17) =18859678a(18) =80014835a(19) =348776577a(20) =1559776269a(21) =7147792819a(22) =33526120083a(23) =160785623546a(24) =787685471323