  The coefficients of certain operators on $V\otimes V$ can be constructed
using generating functions. Necessary and sufficient conditions are given for
some such operators to satisfy the Yang-Baxter equation. As a corollary we
obtain a simple, direct proof that the Cremmer-Gervais R-matrices satisfy the
Yang-Baxter equation. This approach also clarifies Cremmer and Gervais's
original proof via the dynamical Yang-Baxter equation.
