a(1) = 1; a(n) = Sum_{d|n, d < n} p(n/d) * a(d), where p = A000041 (partition numbers).

Terms

a(0) =1a(1) =2a(2) =3a(3) =9a(4) =7a(5) =23a(6) =15a(7) =50a(8) =39a(9) =70a(10) =56a(11) =187a(12) =101a(13) =195a(14) =218a(15) =420a(16) =297a(17) =625a(18) =490a(19) =949a(20) =882a(21) =1226a(22) =1255a(23) =2533a(24) =2007a(25) =2840a(26) =3217a(27) =4588a(28) =4565a(29) =6966