a(n) = Sum_{k=0..n}(k!*(n - k)!)/(floor(k/2)!*floor((n - k)/2)!)^2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =28a(5) =96a(6) =160a(7) =512a(8) =896a(9) =2560a(10) =4864a(11) =12288a(12) =25600a(13) =57344a(14) =131072a(15) =262144a(16) =655360a(17) =1179648a(18) =3211264a(19) =5242880a(20) =15466496a(21) =23068672a(22) =73400320a(23) =100663296a(24) =343932928a(25) =436207616a(26) =1593835520a(27) =1879048192a(28) =7314866176a(29) =8053063680