a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =2a(4) =1a(5) =12a(6) =5a(7) =30a(8) =61a(9) =64a(10) =281a(11) =314a(12) =857a(13) =1812a(14) =2701a(15) =7606a(16) =11925a(17) =26376a(18) =55393a(19) =96402a(20) =223985a(21) =405276a(22) =835989a(23) =1726158a(24) =3233133a(25) =6901328a(26) =13260073a(27) =26731882a(28) =54453001a(29) =105630628