a(n) = Sum_{i=0..n} binomial(2*n-i, n+i).

Terms

a(0) =1a(1) =2a(2) =7a(3) =25a(4) =92a(5) =344a(6) =1300a(7) =4950a(8) =18955a(9) =72905a(10) =281403a(11) =1089343a(12) =4227273a(13) =16438345a(14) =64037453a(15) =249855417a(16) =976205516a(17) =3818779616a(18) =14954876080a(19) =58623077586a(20) =230007291334a(21) =903164858092