  We calculate moments of the so-called Kesten distribution by means of the
expansion of the denominator of the density of this distribution and then
integrate all summands with respect to the semicircle distribution. By
comparing this expression with the formulae for the moments of Kesten's
distribution obtained by other means, we find identities involving polynomials
whose power coefficients are closely related to Catalan numbers, Catalan
triangles, binomial coefficients. Finally, as applications of these identities
we obtain various interesting relations between the aforementioned numbers,
also concerning Lucas, Fibonacci and Fine numbers.
