a(n) = Sum_{k=0..n} binomial(2*k,k).

Terms

a(0) =1a(1) =3a(2) =9a(3) =29a(4) =99a(5) =351a(6) =1275a(7) =4707a(8) =17577a(9) =66197a(10) =250953a(11) =956385a(12) =3660541a(13) =14061141a(14) =54177741a(15) =209295261a(16) =810375651a(17) =3143981871a(18) =12219117171a(19) =47564380971a(20) =185410909791a(21) =723668784231