[growth of A000081]

[Christian G.Bower]

D.Broadhurst at open.ac.uk (David Broadhurst) wrote:
> Let a(n) be the number of rooted trees with n nodes, as in EIS A000081.
> Let c=\lim_{n\to\infty} a(n+1)/a(n). Then to 920 digits, I find that c=

> 2.95576528565199497471481752412319...

> Can this constant be related to others? So far, I failed to identify it.

It's known as one of Otter's tree enumeration constants.

Steve Finch has an article on his website at:

http://www.mathsoft.com/asolve/constant/otter/otter.html

The article is linked from A000055 (trees).

Well, Jud, the average of e and pi doesn't seem close enough to explain
it but it is interesting it's so close.

The same can be said for 3 though.

Christian


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