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

Terms

a(0) =2a(1) =1a(2) =1a(3) =2a(4) =4a(5) =8a(6) =18a(7) =40a(8) =88a(9) =194a(10) =460a(11) =1080a(12) =2514a(13) =5840a(14) =14256a(15) =34450a(16) =82552a(17) =197696a(18) =489714a(19) =1204736a(20) =2945128a(21) =7188018a(22) =18002376a(23) =44805640a(24) =110894770a(25) =274209616a(26) =691588200a(27) =1736001314a(28) =4338383356a(29) =10827952192