sidef-scripts/Math/bernoulli_numbers_from_factorials.sf

#!/usr/bin/ruby

# Author: Daniel "Trizen" Șuteu
# Date: 02 December 2017
# https://github.com/trizen

# A new algorithm for computing Bernoulli numbers.

# Inspired from Norman J. Wildberger video lecture:
#   https://www.youtube.com/watch?v=qmMs6tf8qZ8

# See also:
#   https://en.wikipedia.org/wiki/Bernoulli_number#Connection_with_Pascal’s_triangle

func bernoulli_numbers(n) {

    var B = [1]

    for i in (1 .. n) {
        for k in (0 ..^ i) {
            B[i] := 0 -= (B[k] / (i - k + 1)!)
        }
    }

    B.map_kv { |k,v| v * k! }
}

var B = bernoulli_numbers(100)

for k,v in (B.kv) {
    say "B(#{k}) = #{v.as_rat}"
}