Consider the description in Wolfram Alpha of a "third kind" of Euler Transform (http://mathworld.wolfram.com/EulerTransform.html), expressions (5), (7), and (8):
(5) $1+\sum_{n=1}^\infty b_nx^n=\prod_{i=1}^\infty\frac{1}{(1-x^i)^{a_i}}$
(7) $c_n=\sum_{d|n}da_d$
(8) $b_n = \frac{1}{n}(c_n+\sum_{k=1}^{n-1}c_kb_{n-k})$
Could someone please refer me to some literature or help me understand how to derive expression (8) ?