a(n) = (2+[n/2])*n!/((1+[n/2])*[n/2]!^2).

Terms

a(0) =2a(1) =2a(2) =3a(3) =9a(4) =8a(5) =40a(6) =25a(7) =175a(8) =84a(9) =756a(10) =294a(11) =3234a(12) =1056a(13) =13728a(14) =3861a(15) =57915a(16) =14300a(17) =243100a(18) =53482a(19) =1016158a(20) =201552a(21) =4232592a(22) =764218a(23) =17577014a(24) =2912168a(25) =72804200a(26) =11143500a(27) =300874500a(28) =42791040a(29) =1240940160