If I have given the following generating function
$B = \sum_{n > 0} x^n \sum_{k_1 + \cdots + k_c = n} a(k_1) \cdots a(k_c)$
is it possible to obtain a nice convolution expression for $a(k_1) \cdots a(k_c)$ in terms of some generating function A?
What bothers me is the summation-constraint $k_1 + \cdots + k_c = n$ of the inner sum, thus it is not straight forward for me to come up with a convolution.