The Poisson Binomial Distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The first four moments of this distribution are shown in the figure (source: https://en.wikipedia.org/wiki/Poisson_binomial_distribution).
Suppose we are not dealing with a series of typical Bernoulli trials. Rather, suppose we are dealing with trials, where each Bernoulli Distribution $i$ is multiplied by constant, $c_i$, such that some trials are essential weighted more than others.
What are the moments of this more general Poisson Binomial Distribution?