a(n) = C(4*n,n) - C(4*n,n-4).

Terms

a(0) =1a(1) =4a(2) =28a(3) =220a(4) =1819a(5) =15484a(6) =134320a(7) =1180764a(8) =10482340a(9) =93766288a(10) =843822148a(11) =7631018564a(12) =69291185474a(13) =631334484200