On the number of words in the language {w in sigma* | W = wR}2

Let S be the set of all palindromes over @S^*. It is well known, that the language S^2 is an ultralinear, inherently ambiguous context-free language. In this paper we derive an explicit expression for the number of words of length n in S^2. Furthermore, we show, that for card(@S) > 1 the asymptotical density of the language S^2 is zero and that, in the average, each word w of length n in S^2 has exactly one factorization into two palindromes for large n; the variance is zero for large n. Finally, we compute an expression for the structure-generating- function T(S^2;z) of the language S^2; it remains the open problem, if T(S^2;z) is a transcendental or an algebraic function.