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**Pinkk** I had an idea like that but I guess I got too caught up with the suggested hint because it says to consider that $\displaystyle g(x)=f(x^{2})$ where $\displaystyle f(x) = e^{-1/x}$ and then show that $\displaystyle g^{(n)}$ is actually a series of products, where the each product is $\displaystyle f^{(k)}(x^{2})p_{kn}$. That notation of $\displaystyle p_{kn}$ completely through me off, never seen that before and not sure where to begin, but if it can be done more simply as a single polynomial of $\displaystyle 1/x$ times $\displaystyle e^{-1/x^{2}}$, I much rather do that.