a(n) = n + max{ a(i)*a(n-i) ; 1 <= i <= n-1 }, a(n) = n for n <= 2.

Terms

a(0) =1a(1) =2a(2) =5a(3) =9a(4) =15a(5) =31a(6) =52a(7) =89a(8) =164a(9) =289a(10) =479a(11) =973a(12) =1625a(13) =2773a(14) =5099a(15) =8975a(16) =15045a(17) =30181a(18) =50615a(19) =86617a(20) =159593a(21) =281219a(22) =469648a(23) =946753a(24) =1581150a(25) =2698155a(26) =4961354a(27) =8732703a(28) =14638814a(29) =29366143