Actually I'm not sure I have any O(n!) algorithms. There are two places I could have. One of them I capped n, the other I sped up to 2^n n^2
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@propensive Yeah, it's easy to see that for n > m you have n! > m! m^{n - m}, so n! grows faster than any exponential.
@DRMacIver Yep. I quit maths for compsci after two years. It was "vague" before, and has remained so, alas. (And likely always will, now.)