The Akiyama-Tanigawa algorithm for Bernoulli numbers.
Poly-Bernoulli numbers
By using polylogarithm series, we define “poly-Bernoulli numbers” which generalize classical Bernoulli numbers. We derive an explicit formula and a duality theorem for these numbers, together with a von Staudt-type theorem for di-Bernoulli numbers and another proof of a theorem of Vandiver.
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