Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.9

The Akiyama-Tanigawa algorithm for Bernoulli numbers

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.

(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.