A050513 a(n) = (-1)^n * Sum_{i=0..n} binomial(n+1,i+1)*prime(i+1).

2, -7, 20, -53, 136, -341, 836, -2005, 4712, -10881, 24770, -55763, 124464, -275933, 608282, -1334119, 2911870, -6325091, 13674120, -29425307, 63042232, -134517425, 285984130, -606056545, 1280778342, -2700105565, 5680099084, -11925792491