a(n) = A000016(2*n).

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =16a(5) =52a(6) =172a(7) =586a(8) =2048a(9) =7286a(10) =26216a(11) =95326a(12) =349536a(13) =1290556a(14) =4793492a(15) =17895736a(16) =67108864a(17) =252645136a(18) =954437292a(19) =3616814566a(20) =13743895360a(21) =52357696956a(22) =199911205052a(23) =764877654106