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

Terms

a(0) =2a(1) =1a(2) =3a(3) =6a(4) =12a(5) =33a(6) =84a(7) =204a(8) =507a(9) =1410a(10) =3828a(11) =10185a(12) =27048a(13) =78720a(14) =222051a(15) =613770a(16) =1704360a(17) =4978050a(18) =14312460a(19) =40615440a(20) =115306545a(21) =341021994a(22) =994082808a(23) =2865120612a(24) =8271370236a(25) =24556630128a(26) =72215184450a(27) =210645965832a(28) =614238371328