a(n) = [x^n] (1/(1 - x)^n)*Sum_{k>=1} prime(k)*x^k.

Terms

a(0) =0a(1) =2a(2) =7a(3) =26a(4) =97a(5) =366a(6) =1388a(7) =5288a(8) =20225a(9) =77618a(10) =298766a(11) =1153018a(12) =4460072a(13) =17287558a(14) =67129566a(15) =261095420a(16) =1016994627a(17) =3966529870a(18) =15488964428a(19) =60549061804a(20) =236932924494a(21) =927984726826