Short Haskell implementation of the Akiyama-Tanigawa algorithm for computing Bernoulli numbers.

akiyama-tanigawa-bernoulli.hs

{-- Implementation of the Akiyama-Tanigawa algorithm
	for computing Bernoulli numbers. --}

{-- Implement the algorithm by:
	1. Begin with list of reciprocals of positive integers.
	2. Write function to get next row and iteratie it to get list of lists.
	3. Take the head of each list in the list to get Bernoulli nums.
	Everything evaluates lazily, so we can do this nicely with infinite lists. 

	See tkmh.space/flotsam/haskell-akiyama-tanigawa for more.--}

import Data.Ratio -- standard functions on rational numbers

bernoulliNums :: [Rational]
bernoulliNums = map head $ iterate nextRow recips where
  recips = map (\n -> 1 % n) [1..] -- reciprocals of integers
  nextRow xs = zipWith (*) [1..] (zipWith (-) xs (drop 1 xs)) -- one-liner for next row; thanks owst

{-- we can then get the first n Bernoulli numbers with 
	`take n bernoulliNums` --}