OEIS A000147: Labeled trees of diameter 5

We zoom in on OEIS A000147, the number of labeled trees with diameter 5. A tree is connected and acyclic; diameter 5 means the farthest apart nodes are five edges apart, and such trees can be visualized as two height-2 rooted trees joined at their roots. We explore why the first six terms are zero, the minimum six nodes required, and how the counting reduces to rooted labeled trees (A00065). We'll touch on the formulas, their connections to rooted trees, and show how Maple/Mathematica code computes the terms, highlighting the OEIS's web of interrelated sequences.

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