a(n) = Sum_{i=1..floor((n+2)/4)} a(2i-1)*a(n-2i+1), with a(1)=2 and a(2)=a(3)=1.

Terms

a(0) =2a(1) =1a(2) =1a(3) =2a(4) =4a(5) =9a(6) =20a(7) =44a(8) =97a(9) =230a(10) =540a(11) =1257a(12) =2920a(13) =7168a(14) =17393a(15) =41806a(16) =100408a(17) =250098a(18) =618124a(19) =1517008a(20) =3716627a(21) =9375710a(22) =23479016a(23) =58419236a(24) =145210076a(25) =368786352a(26) =931600246a(27) =2341625080a(28) =5877503872a(29) =15027036202