\[e^{z}-e_{n-1}(z)={\cfrac{z^{n}}{n!-\cfrac{n!z}{(n+1)+\cfrac{z}{(n+2)-\cfrac{(n%
+1)z}{(n+3)+\cfrac{2z}{(n+4)-}}}}}\cfrac{(n+2)z}{(n+5)+\cfrac{3z}{(n+6)-}}%
\cdots},\]