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

Terms

a(0) =1a(1) =4a(2) =16a(3) =72a(4) =316a(5) =1376a(6) =6016a(7) =26304a(8) =114960a(9) =502464a(10) =2196224a(11) =9599360a(12) =41957312a(13) =183389184a(14) =801566720a(15) =3503527936a(16) =15313395968a(17) =66932560896a(18) =292552200192