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A rooted, labeled tree on $n$ vertices is a tree with vertex set $[n] := \{1,2,\ldots,n\}$ in which one vertex has been designated the root. A leaf of a rooted tree is a vertex $v$ for which either: $...

Would've been a better question for Christmas than Thanksgiving, but alas... Let $t_n$ denote the number of rooted, unlabeled trees on $n$ vertices (OEIS A000081). These are the isomorphism classes of ...

For $n\ge 1$, let $f(n)$ be the number of rooted complete (unordered) binary trees with $n$ leaves labeled from $1$ to $n$ ("complete binary" means that every vertex has either $0$ or $2$ children and ...