a(n) = Sum_{i=1..n+1} prime(i)*Sum_{j=0..i-1} binomial(n,j).

Terms

a(0) =2a(1) =8a(2) =31a(3) =105a(4) =353a(5) =1039a(6) =2961a(7) =7859a(8) =20437a(9) =53015a(10) =131605a(11) =325097a(12) =787137a(13) =1857829a(14) =4334237a(15) =10072829a(16) =23286445a(17) =52990531a(18) =120131489a(19) =270138397a(20) =601071655a(21) =1334201393a(22) =2945054825a(23) =6485229057a(24) =14277775651a(25) =31269827137a(26) =68032540043a(27) =147446383463a(28) =317906538223a(29) =683411440339