A new representation formula for the Bernoulli numbers (Q6585815)

By using the Akiyama-Tanigawa algorithm, the double sequence, and the partial difference equations, the authors give some computational formulas for the Bernoulli numbers involving the sum of consecutive positive integers and the Faulhaber's formula. The authors gave an illustrative example which is related to calculate the of the Bernoulli numbers and the tangent (or the ``Zag'') numbers. They give recurrence relations for these numbers. The also make some useful remarks and observations on these numbers.