If each node of a rooted random binary tree has probability 1/2 of producing two branches, and p(n) is the probability that the height of the tree is n, then p(n) has the following properties:
* p(n) = 2*b(n+1)^2 with b(n) defined as in A076628;
* p(n+1) = p(n)*(1  sqrt(p(n)/2))^2 starting from p(0)=1/2;
* Sum_n p(n) = 1;
* Sum_n n*p(n) is infinite;
* p(n) = a(n) / 2^(2^(n+1)1).
