  In this paper we propose a new, simple and explicit mechanism allowing to
derive Stein operators for random variables whose characteristic function
satisfies a simple ODE. We apply this to study random variables which can be
represented as linear combinations of (non necessarily independent) gamma
distributed random variables. The connection with Malliavin calculus for random
variables in the second Wiener chaos is detailed. An application to McKay Type
I random variables is also outlined.
