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

Terms

a(0) =1a(1) =6a(2) =22a(3) =96a(4) =428a(5) =1864a(6) =8136a(7) =35584a(8) =155536a(9) =679776a(10) =2971232a(11) =12986880a(12) =56763584a(13) =248105088a(14) =1084430464a(15) =4739883008a(16) =20717318400a(17) =90552296960a(18) =395790530048