Number of partitions of n not having depth 1; see Comments.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =3a(5) =5a(6) =6a(7) =11a(8) =10a(9) =17a(10) =19a(11) =30a(12) =34a(13) =50a(14) =54a(15) =89a(16) =97a(17) =126a(18) =160a(19) =215a(20) =254a(21) =339a(22) =409a(23) =549a(24) =649a(25) =838a(26) =997a(27) =1286a(28) =1562a(29) =1934