  Using a simple identity between various partial derivatives of the energy of
the vector model in 0+0 dimensions, we derive explicit results for the
coefficients of the large N expansion of the model. These coefficients are
functions in a variable $\rho^2$, which is the expectation value of the two
point function in the limit $N=\infty$. These functions are analytic and have
only one (multiple) pole in $\rho^2$. We show to all orders that these
expressions obey a given general formula. Using this formula it is possible to
derive the double scaling limit in an alternative way. All the results obtained
for the double scaling limit agree with earlier calculations. (to be published
in Physics Letters B)
