  The reduced Kronecker coefficients are particular instances of Kronecker
coefficients that contain enough information to recover them. In this notes we
compute the generating function of a family of reduced Kronecker coefficients.
We also gives its connection to the plane partitions, which allows us to check
that this family satisfies the saturation conjecture for reduced Kronecker
coefficients, and that they are weakly increasing. Thanks to its generating
function we can describe our family by a quasipolynomial, specifying its degree
and period.
