  We obtain a Stein characterisation of the distribution of the product of two
correlated normal random variables with non-zero means, and more generally the
distribution of the sum of independent copies of such random variables. Our
Stein characterisation is shown to naturally generalise a number of other Stein
characterisations in the literature. From our Stein characterisation we derive
recursive formulas for the moments of the product of two correlated normal
random variables, and more generally the sum of independent copies of such
random variables, which allows for efficient computation of higher order
moments.
