a(n) = p(P(n)), P = primes (A000040), p = partition numbers (A000041).

Terms

a(0) =2a(1) =3a(2) =7a(3) =15a(4) =56a(5) =101a(6) =297a(7) =490a(8) =1255a(9) =4565a(10) =6842a(11) =21637a(12) =44583a(13) =63261a(14) =124754a(15) =329931a(16) =831820a(17) =1121505a(18) =2679689a(19) =4697205a(20) =6185689a(21) =13848650a(22) =23338469a(23) =49995925a(24) =133230930a(25) =214481126a(26) =271248950a(27) =431149389a(28) =541946240a(29) =851376628