G.f.: A(x) = x/(1 - (1-3x)*A( x/(1-3x) )).

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =44a(5) =288a(6) =2172a(7) =18516a(8) =175352a(9) =1819868a(10) =20491844a(11) =248417128a(12) =3221797252a(13) =44464876996a(14) =650076797232