a(n) = Sum_{k=0..n} 2^k * binomial(2*k+1,2*n-2*k).

Terms

a(0) =1a(1) =2a(2) =10a(3) =48a(4) =204a(5) =888a(6) =3896a(7) =17024a(8) =74384a(9) =325152a(10) =1421216a(11) =6211840a(12) =27151040a(13) =118673280a(14) =518702976a(15) =2267172864a(16) =9909473536a(17) =43312824832a(18) =189313870336a(19) =827462578176