a(n) = 3*L(2*n)/5 - (-1)^n/5, where L = A000032.

Terms

a(0) =1a(1) =2a(2) =4a(3) =11a(4) =28a(5) =74a(6) =193a(7) =506a(8) =1324a(9) =3467a(10) =9076a(11) =23762a(12) =62209a(13) =162866a(14) =426388a(15) =1116299a(16) =2922508a(17) =7651226a(18) =20031169a(19) =52442282a(20) =137295676a(21) =359444747a(22) =941038564a(23) =2463670946a(24) =6449974273a(25) =16886251874a(26) =44208781348a(27) =115740092171