OEIS A000169: Labeled rooted trees on n nodes

We explore A000169, the number of labeled rooted trees with n nodes, given by n^{n-1}. We'll unpack why labeling and rooting matter, sketch the Cayley-style intuition, and glimpse surprising connections: bijections with certain digraphs, functional-graph representations of maps [n]→[n], and other areas where this simple formula keeps reappearing in combinatorics and algebra.

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