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Computation of binomial #172
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Currently the text book formula
is used to compute binomial coefficients.
I suggest using the algorithm below.
The text is from [1].
Binomial Coefficients
Binomial coefficients C(n,k) are calculated by first arranging k <= n/2 using C(n,k) = C(n,n-k) if necessary, and then evaluating the following product simply from i=2 to i=k.
It's easy to show that each denominator i will divide the product so far, so the exact division algorithm is used (see Exact Division).
[1] https://web.archive.org/web/20111229055708/https://www.gnu.org/software/gmp/manual/html_node/Binomial-Coefficients-Algorithm.html
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