I am concerned about the  following question, consider$P_n(x)= \sum_{i=0}^n \frac{x^n}{n!}$Is there a straight line program (or arithmetic circuits) of polynomial size (wrt $n$) for the  polynomial $P_{2^n}(x)$? The difficulty seems to lie in the factorial, as for example the polynomial $x^{2^n}$ has a polynomial size arithmetic circuit (by repeated squaring). Sorry in my previous post I did not make the question clear, as it would become a very simple question. 
arithmetic circuits for polynomials (updated)
cc.complexity theory;arithmetic circuits