sidef-scripts/Math/bernoulli_numbers_from_pascal_triangle.sf

#!/usr/bin/ruby

# Computing Bernoulli numbers from Pascal's triangle

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

func pascal_bernoulli_number(n) {

    var A = []

    for i in (0 ..^ n) {
        for k in (0 ..^ n) {
            A[i][k] = (k > i+1 ? 0 : binomial(i+2, k))
        }
    }

    A.det / (n+1)!
}

for n in (0..30) {
    say "B(#{n}) = #{pascal_bernoulli_number(n).as_rat}"
}