a(n) = Sum_{k=1..n} binomial(2*k, k) * A000005(k).

Terms

a(0) =2a(1) =14a(2) =54a(3) =264a(4) =768a(5) =4464a(6) =11328a(7) =62808a(8) =208668a(9) =947692a(10) =2358556a(11) =18583492a(12) =39384692a(13) =199851092a(14) =820321172a(15) =3825723122a(16) =8492935562a(17) =62943747362a(18) =133634274962a(19) =960713447882