Essentially a duplicate of A000129.

Terms

a(0) =2a(1) =5a(2) =12a(3) =29a(4) =70a(5) =169a(6) =408a(7) =985a(8) =2378a(9) =5741a(10) =13860a(11) =33461a(12) =80782a(13) =195025a(14) =470832a(15) =1136689