Wedderburn-Etherington number

The $n$th Wedderburn-Etherington number counts how many weakly binary trees can be constructed such that each graph vertex (not counting the root vertex) is adjacent to no more than three other such vertices, for a given number $n$ of nodes. The first few Wedderburn-Etherington numbers are 1, 1, 1, 2, 3, 6, 11, 23, 46, 98, 207, 451, 983, etc. listed in A001190 of Sloane’s OEIS. Michael Somos gives the following recurrence relations:

$$a_{2n}=\frac{1}{2}{a}_n{a}_{n+1}+\sum _{i=1}^n{a}_i{a}_{2n-i}$$

and

$$a_{2n-1}=\sum _{i=0}^{n-1}{a}_{i+1}{a}_{2n-i}$$

with $a_1=a_2=1$ in both relations.

Title	Wedderburn-Etherington number
Canonical name	WedderburnEtheringtonNumber
Date of creation	2013-03-22 16:49:32
Last modified on	2013-03-22 16:49:32
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	6
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 05A15
Synonym	Wedderburn Etherington number
Synonym	Etherington-Wedderburn number