Number of compositions of n where the largest part is less than the number of parts.

Terms

a(0) =0a(1) =1a(2) =1a(3) =4a(4) =8a(5) =17a(6) =38a(7) =83a(8) =174a(9) =367a(10) =771a(11) =1606a(12) =3324a(13) =6849a(14) =14054a(15) =28743a(16) =58605a(17) =119161a(18) =241717a(19) =489345a(20) =988945a(21) =1995604a(22) =4021710a(23) =8095815a(24) =16281400a(25) =32716231a(26) =65694106a(27) =131833462a(28) =264423116a(29) =530128036