]> $$\begin{array}{rcl}f\left(k+1;r,n,N\right)& =& \frac{\left(n-k\right)\left(r-k\right)}{\left(k+1\right)\left(N-n-r+k+1\right)}f\left(k;r,n,N\right)\\ f\left(k-1;r,n,N\right)& =& \frac{x\left(N-n-r+k\right)}{\left(n-k+1\right)\left(r-k+1\right)}f\left(k;r,n,N\right)\end{array}$$