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

Terms

a(0) =2a(1) =-7a(2) =20a(3) =-53a(4) =136a(5) =-341a(6) =836a(7) =-2005a(8) =4712a(9) =-10881a(10) =24770a(11) =-55763a(12) =124464a(13) =-275933a(14) =608282a(15) =-1334119a(16) =2911870a(17) =-6325091a(18) =13674120a(19) =-29425307a(20) =63042232a(21) =-134517425a(22) =285984130a(23) =-606056545a(24) =1280778342a(25) =-2700105565a(26) =5680099084a(27) =-11925792491