a(n) = Sum_{k=0..n} floor(binomial(n,k)/(k+1)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =9a(5) =18a(6) =30a(7) =56a(8) =101a(9) =186a(10) =339a(11) =630a(12) =1167a(13) =2182a(14) =4092a(15) =7710a(16) =14561a(17) =27594a(18) =52425a(19) =99862a(20) =190647a(21) =364722a(22) =699045a(23) =1342176a(24) =2581107a(25) =4971024a(26) =9586975a(27) =18512790a(28) =35791386a(29) =69273666