Guichard-Combinatorics-Graph-Theory · Problem 1.8.11
Fundamentals
Mathematics — Probability · stirling-numbers
Problem
Under the assumptions that s(n,0)=s(0,n)=0 for n=0, and s(n,k)=s(n−1,k−1)−(n−1)s(n−1,k), extend the table for s(n,k) to all integers, and find a connection to S(n,k) similar to that in the previous problem.