Binomial transform of floor(n/2)!.

Terms

a(0) =1a(1) =2a(2) =4a(3) =8a(4) =17a(5) =38a(6) =90a(7) =224a(8) =585a(9) =1594a(10) =4520a(11) =13288a(12) =40409a(13) =126782a(14) =409646a(15) =1360512a(16) =4637681a(17) =16202034a(18) =57941164a(19) =211860488a(20) =791272129a(21) =3015807254a(22) =11719800674a(23) =46401584096a(24) =187039192185a(25) =767058993386