B Best fit curve associated with the combination formula

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Sorry if this is more of a HW question (if so then moderator please move my question. Thanks!)

Hi, I'm trying to get an expression for a best fit curve of the combination formula (##_nC_r##).
As far as I can tell, the curve is a simple parabolic curve, and its shape doesn't change. It's just scaled depending on ##n##.

How might I get the continuous form of the discrete combination formula?
 
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It is not a parabola.

The generalization of factorials to the real numbers is the gamma function.
 
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