Thanks, Matthew! I want to take Greg Egan's formula and convert it from gamma functions to factorials. Let me at least take the first step: converting it to LaTeX:

$\text{moment}(d,n) = \frac{2^{d+n-2} \Gamma(\frac{d}{2}) \Gamma(\frac{1}{2} (d+n-1))}{\sqrt{\pi} \, \Gamma(d+ \frac{n}{2} - 1)}$