  In this paper we study the moment generating function and the moments of
occupation time functionals of one-dimensional diffusions. Assuming,
specifically, that the process lives on $\mathbb{R}$ and starts at~0, we apply
Kac's moment formula and the strong Markov property to derive an expression for
the moment generating function in terms of the Green kernel of the underlying
diffusion. Moreover, the approach allows us to derive a recursive equation for
the Laplace transforms of the moments of the occupation time on $\mathbb{R}_+$.
If the diffusion has a scaling property, the recursive equation simplifies to
an equation for the moments of the occupation time up to time 1. As examples of
diffusions with scaling property we study in detail skew two-sided Bessel
processes and, as a special case, skew Brownian motion. It is seen that for
these processes our approach leads to simple explicit formulas. The recursive
equation for a sticky Brownian motion is also discussed.
