Calculate the expected number of elements in a rooted ordered unlabeled binary tree of maximum depth d; see https://math.stackexchange.com/questions/2836730

Question2836730.java

import java.math.BigInteger;

public class Question2836730 {
	public static void main (String [] args) {
		BigInteger a = BigInteger.ONE;
		BigInteger s = BigInteger.ZERO;
		
		for (int d = 1;;d++) {
			BigInteger square = a.multiply (a);
			BigInteger sn = s.multiply (a).multiply (BigInteger.TWO).add (square);
			BigInteger an = square.add (BigInteger.ONE);
			BigInteger ds = sn.subtract (s);
			BigInteger da = an.subtract (a);
			double mean = ds.doubleValue () / da.doubleValue ();
			System.out.println (d + "&" + sn.doubleValue () / an.doubleValue () + "&" + mean + "&" + (mean + 1) / Math.pow (2,d) + "\\\\");
			a = an;
			s = sn;
		}
	}
}