Geodesic
The Akiyama-Tanigawa algorithm for Bernoulli numbers
Journal of integer sequences, Tome 3 (2000) no. 2
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.
Classification : 11B68, 11B73
Mots-clés : Akiyama-Tanigawa algorithm, Bernoulli numbers, Stirling numbers, poly-Bernoulli numbers 
@article{JIS_2000__3_2_a1,
     author = {Kaneko,  Masanobu},
     title = {The {Akiyama-Tanigawa} algorithm for {Bernoulli} numbers},
     journal = {Journal of integer sequences},
     year = {2000},
     volume = {3},
     number = {2},
     zbl = {0982.11009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2000__3_2_a1/}
}
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Kaneko,  Masanobu. The Akiyama-Tanigawa algorithm for Bernoulli numbers. Journal of integer sequences, Tome 3 (2000) no. 2. http://geodesic.mathdoc.fr/item/JIS_2000__3_2_a1/