Wedderburn-Etherington number

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z) = sum_(i = 0)^∞ g_i z^i, be the generating function for the number of weakly binary trees on i nodes, where g_0 | = | 0 g_1 | = | g_2 = g_3 = 1 g_(2i + 1) | = | sum_(j = 1)^i g_(2i + 1 - j) g_j g_(2i) | = | 1/2 g_i(g_i + 1) + sum_(j = 1)^(i - 1) g_(2i - j) g_j.

binary tree | rooted tree | strongly binary tree | tree