Number of finite sequences of integer partitions with total sum n and all distinct lengths.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =11a(5) =23a(6) =49a(7) =103a(8) =214a(9) =434a(10) =874a(11) =1738a(12) =3443a(13) =6765a(14) =13193a(15) =25512a(16) =48957a(17) =93267a(18) =176595a(19) =332550a(20) =622957a(21) =1161230a(22) =2153710a(23) =3974809a(24) =7299707a(25) =13343290a(26) =24280924a(27) =43999100a(28) =79412942a(29) =142792535