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

Terms

a(0) =1a(1) =3a(2) =13a(3) =60a(4) =277a(5) =1278a(6) =5896a(7) =27201a(8) =125491a(9) =578949a(10) =2670964a(11) =12322413a(12) =56849086a(13) =262271568a(14) =1209982081a(15) =5582216355a(16) =25753389181a(17) =118812495276a(18) =548137914373