a(n) = binomial(4*n+1,n)*2/(3*n+2).

Terms

a(0) =1a(1) =2a(2) =9a(3) =52a(4) =340a(5) =2394a(6) =17710a(7) =135720a(8) =1068012a(9) =8579560a(10) =70068713a(11) =580034052a(12) =4855986044a(13) =41043559340a(14) =349756577100