A number n taken to the falling factorial power k is defined as n*(n-1)*...*(n-k+1). We will denote it by n^^k. For example, 7^^3=7*6*5=210. By definition, n^^1=n.
We will now continue this definition to the non-positive values of k using the following fact: (n-k)*(n^^k)=n^^(k+1), or, in other words, n^^k=(n^^(k+1))/(n-k). It is directly derived from the above definition.
By using it, we find:
For example, 3^^(-1)=1/4=0.25, 2^^(-3)=1/3/4/5=1/60=0.016666...
- and, in general, n^^(-k)=1/(n+1)/(n+2)/.../(n+k).
Given a positive int n and an int k, return a double containing the value of n taken to the falling factorial power of k.