a(n) = 3^n*Sum_{ k=0..n } binomial(2*k,k)/3^k.

Terms

a(0) =1a(1) =5a(2) =21a(3) =83a(4) =319a(5) =1209a(6) =4551a(7) =17085a(8) =64125a(9) =240995a(10) =907741a(11) =3428655a(12) =12990121a(13) =49370963a(14) =188229489a(15) =719805987a(16) =2760498351a(17) =10615101273a(18) =40920439119a(19) =158106581157a(20) =612166272291