Counting and recounting (Q790816)

An expository article concerning combinatorial identities and their ''natural'' interpretations, written with a light touch and enjoyable to read. Included are identities involving products, summations and inclusion/exclusion. The author concludes by challenging the reader to find the ''natural'' meaning of the identity \(4^ n=\sum^{h}_{r=0}\left( \begin{matrix} 2r\\ r\end{matrix} \right)\left( \begin{matrix} 2n-2r\\ n-r\end{matrix} \right).\)