a(1) = 1; a(n+1) = Sum_{k=1..n} a(k) * ceiling(n/k).

Terms

a(0) =1a(1) =1a(2) =3a(3) =8a(4) =20a(5) =50a(6) =121a(7) =297a(8) =716a(9) =1739a(10) =4198a(11) =10157a(12) =24513a(13) =59246a(14) =143006a(15) =345381a(16) =833792a(17) =2013272a(18) =4860337a(19) =11734717a(20) =28329772a(21) =68396030a(22) =165121957a(23) =398644144a(24) =962410246a(25) =2323475153a(26) =5609360573a(27) =13542220814a(28) =32693802921a(29) =78929886033