Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles
Abstract
It is shown that Bernoulli numbers and tangent numbers (the derivatives of the tangent function at zero) can be obtained by means of easily defined triangles of numbers in several ways, some of them very similar to the Catalan triangle and a Motzkinlike triangle. Our starting point in order to show this is a new expression of Zeta(2n) involving Motzkin paths.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:math/0109108
 Bibcode:
 2001math......9108A
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Combinatorics;
 11B68 (Primary);
 11B75 (Secondary)