Combinatorics and Graph Theory · Problem 1.8.9

Fundamentals — David Guichard

Mathematics — Combinatorics · stirling-numbers-first-kind

Problem

Use the previous exercise to prove s(n,k)=∑i=k−1n−1(−1)n−i−1(n−i−1)!(n−1i)s(i,k−1)s(n,k) = \displaystyle\sum_{i=k-1}^{n-1} (-1)^{n-i-1}(n-i-1)!\binom{n-1}{i}s(i,k-1).

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