a(n) = Sum_{k=0..n} 3^k * binomial(2*n+1,n-k).

Terms

a(0) =1a(1) =6a(2) =34a(3) =188a(4) =1026a(5) =5556a(6) =29940a(7) =160824a(8) =862018a(9) =4613636a(10) =24667644a(11) =131795912a(12) =703812916a(13) =3757135752a(14) =20051429544a(15) =106992663408a(16) =570827898306