How to sum the following series $\frac {x} {2!(n-2)!}+\frac {x^{2}} {5!(n-5)!}+\frac {x^{3}} {8!(n-8)!}+\dots +\frac {x^{\frac{n}{3}}} {(n-1)!}$ n being a multiple of 3.
This question is from a book, i did not make this up. I can see a pattern in each term as the ith term can be written as $\frac {x^i}{(3i-1)!(n+1-3i)!}$
but i am unsure what it going on with the indexing variable's range. Any help would be much appreciated ?