Logarithm of e.g.f. for primes.

Terms

a(0) =2a(1) =-1a(2) =3a(3) =-12a(4) =59a(5) =-354a(6) =2535a(7) =-21190a(8) =202731a(9) =-2183462a(10) =26130441a(11) =-343956264a(12) =4938891841a(13) =-76827253854