a(n) = 1 + Sum_{k=1..n} Sum_{d|k} mu(k/d)*p(d), where p(d) = number of partitions of d (A000041).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =14a(6) =21a(7) =35a(8) =52a(9) =79a(10) =113a(11) =168a(12) =231a(13) =331a(14) =450a(15) =617a(16) =826a(17) =1122a(18) =1469a(19) =1958a(20) =2540a(21) =3315a(22) =4260a(23) =5514a(24) =6995a(25) =8946a(26) =11280a(27) =14260a(28) =17840a(29) =22404