This is the coefficient of the $x^k$ term in the polynomial expansion of the binomial power $(1 + x)^n$. This is also the so called choose function of n and k (nchoosek in MATLAB), i.e. the number of k-element subsets (the k-combinations) of a set of n objects. When a coefficient is large, results may be inexact.

The result is only accurate to 15 digits for double-precision inputs in 32bits computers.