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

Terms

a(0) =1a(1) =0a(2) =3a(3) =6a(4) =6a(5) =40a(6) =34a(7) =140a(8) =295a(9) =440a(10) =1533a(11) =2210a(12) =5812a(13) =12544a(14) =22212a(15) =58104a(16) =103421a(17) =233296a(18) =499367a(19) =957246a(20) =2196050a(21) =4265208a(22) =9077206a(23) =19147812a(24) =38083843a(25) =82195784a(26) =165218433a(27) =343559002a(28) =715871584a(29) =1447170704