Motzkin Numbers

In this paper Motzkin numbersMn(which are related to Catalan numbers) are studied. The (known) connection to Tchebychev polynomials is discussed with applications to the Hankel matrices of Motzkin numbers. It is shown that the sequenceMnis logarithmically concave with limMn + 1 / Mn = 3. Finally, two ballot-number type sequences forMnare derived, with an application to directed animals.