A038066 prod{k=1..inf}(1/(1-x^k)^a(k)) = 1+5x.

5, -15, 40, -150, 624, -2620, 11160, -48750, 217000, -976872, 4438920, -20343700, 93900240, -435970980, 2034504992, -9536718750, 44878791360, -211927733500, 1003867701480, -4768371093720, 22706531339280