Floor-Sqrt transform of Sylvester continuants (A002801).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =7a(5) =20a(6) =65a(7) =232a(8) =883a(9) =3581a(10) =15383a(11) =69579a(12) =329769a(13) =1631137a(14) =8391824a(15) =44777342a(16) =247182082a(17) =1408611456a(18) =8270902948a(19) =49953724226a(20) =309870713560