  We provide an efficient encoding of the natural numbers {0,1,2,3,...} as
strings of nested parentheses {(),(()),(()()),((())),...}, or considered
inversely, an efficient enumeration of such strings. The technique is based on
the recursive definition of the Catalan numbers. The probability distributions
arising from this encoding are explored. Applications of this encoding to
prefix-free data encoding and recursive function theory are briefly considered.
