A038065 prod{k=1..inf}(1/(1-x^k)^a(k)) = 1+4x.

4, -10, 20, -60, 204, -690, 2340, -8160, 29120, -104958, 381300, -1397740, 5162220, -19175130, 71582716, -268431360, 1010580540, -3817763040, 14467258260, -54975528948, 209430785460, -799645010850, 3059510616420