The attached patch addresses two issues:<div><br></div><div>1. COUNT-PERMUTATIONS now has type-checking and uses %MULTIPLY-RANGE, as was suggested in the comments.</div><div><br></div><div>2. SUBFACTORIAL now produces correct values. Previously, the values returned were incorrect starting with N = 12 or so. This was because the approximate value of e, produced by (exp 1), had insufficient precision be used in the [ n! / e ] formula for the subfactorial !n. Changing (exp 1) to (exp1.0d0) adds precision to e, but the problem still remained for N &gt;= 14 or so. I reimplemented SUBFACTORIAL using the !n = n! * \sum_{k=0}^k{ \frac{ (-1)^k }{ k! } } formula to give exact results.</div>

<div><br></div><div>I also added tests for both of these functions.</div><div><br></div><div>In the near future, I&#39;d like to open up a review of these functions (as well as the other combinatorics functions). Nikodemus suggested a couple of months ago that this should be done, but I wasn&#39;t sure if this was limited to Alexandria&#39;s main developers or open to everyone. </div>

<div><br></div><div>Mason</div><div><br></div>