a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+1,2*n-4*k+1).

Terms

a(0) =1a(1) =0a(2) =3a(3) =2a(4) =5a(5) =20a(6) =11a(7) =70a(8) =93a(9) =176a(10) =515a(11) =618a(12) =1877a(13) =3212a(14) =6043a(15) =14670a(16) =23469a(17) =55336a(18) =104915a(19) =201202a(20) =442213a(21) =801924a(22) =1711787a(23) =3369814a(24) =6574205a(25) =13748896a(26) =26354723a(27) =54064250a(28) =107762933a(29) =212616060