A recursive process computes a function f(n,k)=f(n−1,k−1)+f(n−1,k)f(n, k) = f(n-1, k-1) + f(n-1, k)f(n,k)=f(n−1,k−1)+f(n−1,k) with f(n,0)=1f(n, 0) = 1f(n,0)=1 and f(n,n)=1f(n, n) = 1f(n,n)=1. What does f(n,k)f(n, k)f(n,k) represent?
The nnn-th Fibonacci number
The binomial coefficient (nk)\binom{n}{k}(kn)
The number of derangements of nnn elements
The partition function p(n,k)p(n, k)p(n,k)