Huh. I always thought n! grew faster than c^n which would be even worse than exponential. Maybe enough cancels out to make it simpler than it appears.<p><i>edit</i><p>Actually, for even dimensions it&#x27;s pretty clear.
n = dimension&#x2F;2<p><pre><code>    pi^n &#x2F; n!
</code></pre>
factorial wins. The problem is worse than exponentiation.