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

Terms

a(0) =1a(1) =4a(2) =18a(3) =82a(4) =374a(5) =1704a(6) =7752a(7) =35214a(8) =159750a(9) =723880a(10) =3276908a(11) =14821668a(12) =66991436a(13) =302605528a(14) =1366182276a(15) =6165204102a(16) =27811282374a(17) =125415953208a(18) =565408947756