# Sequence of derivatives [duplicate]

Is it true that every sequence of real numbers $(a_n)$ can be a sequence of derivatives - ($f^{(n)}(0)$) of some function $f\in C^{\infty}(\mathbb{R})$?
It's clear if the series $\sum \frac{a_n}{n!}x^n$ has non-zero radius of convergency, but I didn't manage to prove it for the other cases.
• Don't you want infinitely differentiable just at $0$? – Pedro Tamaroff Feb 25 '14 at 17:37
• I mean, I'm not saying only at $0$; but that that should suffice. – Pedro Tamaroff Feb 25 '14 at 17:40