a(1)=1; for n>1, a(n) = Sum_{k=1..n-1} a(k) * floor(n/k).

Terms

a(0) =1a(1) =2a(2) =5a(3) =13a(4) =27a(5) =62a(6) =125a(7) =266a(8) =538a(9) =1106a(10) =2213a(11) =4509a(12) =9019a(13) =18166a(14) =36365a(15) =73012a(16) =146025a(17) =292658a(18) =585317a(19) =1171783a(20) =2343697a(21) =4689610a(22) =9379221a(23) =18763300a(24) =37526628a(25) =75062278a(26) =150125100a(27) =300268507a(28) =600537015a(29) =1201111598