For dimension $d$, let $N(r,d)$ = number of spheres of radius $r$ which can be packed in a sphere of radius 1.
For dimension 1, $N(r,1) = \lfloor 1/r \rfloor$.
From the articles below, I infer that $N$ does not have a closed form for higher dimensions.
I would like to know more and am looking for a good starting point. Any ideas? Thanks. --Len