bernoulli_numbers_from_pascal_triangle_2.sf

#!/usr/bin/ruby

# Computing Bernoulli numbers from a derivation of Pascal's triangle

# Formula presented by Norman J. Wildberger in his video lecture:
#   https://www.youtube.com/watch?v=jx_JR5xD9Ko

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

func pascal_bernoulli_numbers(n) {

    var A = []

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

    A.inv.column(0)
}

var B = pascal_bernoulli_numbers(30)

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