L.g.f.: log(1 + Sum_{k>=1} prime(k)*x^k) = Sum_{n>=1} a(n)*x^n/n.

Terms

a(0) =2a(1) =2a(2) =5a(3) =2a(4) =12a(5) =-13a(6) =16a(7) =-30a(8) =41a(9) =-18a(10) =46a(11) =-73a(12) =132a(13) =-278a(14) =315a(15) =-318a(16) =580a(17) =-805a(18) =1218a(19) =-1998a(20) =2665a(21) =-3958a(22) =5936a(23) =-7761a(24) =11612a(25) =-17678a(26) =25313a(27) =-38134a(28) =54754a(29) =-76833