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

Terms

a(0) =1a(1) =0a(2) =2a(3) =4a(4) =3a(5) =20a(6) =16a(7) =56a(8) =117a(9) =152a(10) =510a(11) =700a(12) =1671a(13) =3532a(14) =5772a(15) =14480a(16) =24761a(17) =52400a(18) =109114a(19) =198324a(20) =437899a(21) =821828a(22) =1670536a(23) =3423784a(24) =6547325a(25) =13666184a(26) =26654966a(27) =53492716a(28) =108440335a(29) =212433276