Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles

Details Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles

2001-09-17

arxiv.org/abs/math/0109108v1

Mathematics

Number Theory

Scientific paper

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 Motzkin-like triangle. Our starting point in order to show this
is a new expression of Zeta(2n) involving Motzkin paths.

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