a(n) = floor(sqrt(2*n!)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =15a(6) =37a(7) =100a(8) =283a(9) =851a(10) =2693a(11) =8934a(12) =30951a(13) =111597a(14) =417560a(15) =1617203a(16) =6468815a(17) =26671611a(18) =113158063a(19) =493244564a(20) =2205856753a(21) =10108505544a(22) =47413093714a(23) =227385209452