Combinatorics and Graph Theory · Problem 1.8.8

Fundamentals — David Guichard

Mathematics — Combinatorics · stirling-numbers-first-kind

Problem

Prove: [nk]=∑i=k−1n−1(n−i−1)!(n−1i)[ik−1]\left[\begin{smallmatrix}n\\k\end{smallmatrix}\right] = \displaystyle\sum_{i=k-1}^{n-1} (n-i-1)!\binom{n-1}{i}\left[\begin{smallmatrix}i\\k-1\end{smallmatrix}\right].

Related theory

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