a(n) = floor(sqrt(n!+1)).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =11a(6) =26a(7) =71a(8) =200a(9) =602a(10) =1904a(11) =6317a(12) =21886a(13) =78911a(14) =295259a(15) =1143535a(16) =4574143a(17) =18859677a(18) =80014834a(19) =348776576a(20) =1559776268a(21) =7147792818a(22) =33526120082a(23) =160785623545a(24) =787685471322