produces a balanced tree with 2^{$1} leaves when $1 is the first command line argument

balanced_tree.py

#!/usr/bin/env python
def balanced_tree(n, level):
    if level == 0:
        return n + 1, 't%d' % n
    n, leftsub = balanced_tree(n, level - 1)
    n, rightsub = balanced_tree(n, level - 1)
    return n, '(%s,%s)' % (leftsub, rightsub)

if __name__ == '__main__':
    import sys
    print balanced_tree(1, int(sys.argv[1]))[1]