a(1)=1, a(n) = Sum_{k=1..n-1} max(a(k), a(n-k)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =40a(6) =118a(7) =349a(8) =1042a(9) =3112a(10) =9322a(11) =27926a(12) =83738a(13) =251096a(14) =753170a(15) =2259161a(16) =6777134a(17) =20330360a(18) =60990038a(19) =182967002a(20) =548897894a(21) =1646684360a(22) =4940043758a(23) =14820103348a(24) =44460282118a(25) =133380762616a(26) =400142204110