a(n) = Sum_{j=1..n} binomial(floor(n/j)+n,n+1).

Terms

a(0) =1a(1) =5a(2) =17a(3) =64a(4) =220a(5) =839a(6) =3061a(7) =11684a(8) =44126a(9) =169432a(10) =648589a(11) =2505411a(12) =9670165a(13) =37497431a(14) =145502481a(15) =566076182a(16) =2204451031a(17) =8599761208a(18) =33581164151a(19) =131296796355a(20) =513812162117