G.f.: Sum_{n>=1} x^n * (1+x)^prime(n).

Terms

a(0) =1a(1) =3a(2) =5a(3) =9a(4) =19a(5) =43a(6) =109a(7) =297a(8) =793a(9) =2059a(10) =5382a(11) =14319a(12) =38897a(13) =110525a(14) =335225a(15) =1067923a(16) =3449922a(17) =11058922a(18) =35087589a(19) =110642516a(20) =346605981a(21) =1072833978a(22) =3270252617a(23) =9869924183a(24) =29933522269a(25) =92890564700a(26) =298225920323a(27) =987831491085