In my opinion is is the same (logic), although maybe "more accurate". 

http://www.boost.org/doc/libs/1_36_0/libs/math/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
binomial uses n!/(n-k)!k! for reasonable values, and fallbacks to beta function for high ones. I couldnt find where the treshold is.

So uness the case for n>=171 was some hack, instead of approximation for binomial, it should work ok. Do you have some tests to excercise and verify this?