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**The Akiyama-Tanigawa algorithm for Bernoulli numbers**

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Masanobu Kaneko

Graduate School of Mathematics

Kyushu University

Fukuoka 812-8581, Japan

Email address: mkaneko@math.kyushu-u.ac.jp

**Abstract:**
A direct proof is given for Akiyama and Tanigawa's algorithm for computing
Bernoulli numbers.
The proof uses a closed formula for Bernoulli numbers expressed in terms of Stirling numbers.
The outcome of the same algorithm with different initial values is also
briefly discussed.

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(The Bernoulli numbers are A027641/A027642.
The table in Figure 1 yields sequences
A051714/A051715.
Other sequences which mention this paper are
A000367,
A002445,
A026741,
A045896,
A051712,
A051713,
A051716,
A051717,
A051718,
A051719,
A051720,
A051721,
A051722,
A051723.)

Received August 7, 2000;
published in Journal of Integer Sequences Dec. 12, 2000.

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