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A tree is a connected graph without cycles, with a finite or infinite number of vertices. There are many variants of trees, according to further constraints or decorations.

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Are the asymptotics of A003238 known?

I'll show that $$ \log a(n) \sim \frac{(\log n)^2}{\log 4} \approx 0.7213\ldots (\log n)^2. $$ So the range for the constant given in the conjecture is false, but an asymptotic of that general sha …
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