a(n) = Sum_{k=floor((n+1)/2)..n} binomial(2*k,k).

Terms

a(0) =1a(1) =2a(2) =8a(3) =26a(4) =96a(5) =342a(6) =1266a(7) =4678a(8) =17548a(9) =66098a(10) =250854a(11) =956034a(12) =3660190a(13) =14059866a(14) =54176466a(15) =209290554a(16) =810370944a(17) =3143964294a(18) =12219099594a(19) =47564314774a(20) =185410843594a(21) =723668533278