require "bignum"
local fmt = require "fmt"

local function bernoulli(n)
    assert(n >= 0, "Argument must be non-negative")
    local a = table.create(n + 1)
    for m = 0, n do
        a[m + 1] = bigrat.recip(m + 1)
        local j = m
        while j >= 1 do
            a[j] = (a[j] - a[j + 1]) * bigrat.int(j)
            j -= 1
        end
    end
    return n != 1 ? a[1] : -a[1]  --'first' Bernoulli number
end

local zero = bigrat.int(0)
for n = 0, 60 do
    local b = bernoulli(n)
    if b != zero then fmt.print("B(%2d) = %44s / %s", n, b:getNum(), b:getDen()) end
end