a(n) = 1 + Max_{0<=i<=j<=k; i+j+k=n-1} a(i)*a(j)*a(k) for n>0, with a(0) = 1.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =9a(5) =13a(6) =21a(7) =37a(8) =55a(9) =91a(10) =163a(11) =244a(12) =406a(13) =730a(14) =1054a(15) =1702a(16) =2998a(17) =4456a(18) =7372a(19) =13204a(20) =19765a(21) =32887a(22) =59131a(23) =85411a(24) =137971a(25) =243091a(26) =361351a(27) =597871a(28) =1070911a(29) =1603081