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Re(2): Pascal triange...by gumby (Scribe) 
on Jun 19, 2002 at 10:40 UTC ( #175615=note: print w/ replies, xml )  Need Help?? 
Ok, it's been communicated that using the entropy function would provide a better approximation to nCr. So here is such a formula: Let H(eps) := eps.log_2(eps)(1eps)log_2(1eps) be a binary entropy function. Then binom(n, eps.n) is approximately equal to 2^(n.H(eps)). Where eps is short for epsilon. Update: Note that this uses the more common Stirling formula which is slightly less accurate as it truncates terms in the series (instead of approximating them like the formula i posted before).
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