a(n) = Sum_{k=0..n} binomial(4*n+4,k).

Terms

a(0) =1a(1) =9a(2) =79a(3) =697a(4) =6196a(5) =55455a(6) =499178a(7) =4514873a(8) =40999516a(9) =373585604a(10) =3414035527a(11) =31278197839a(12) =287191809724