bernoulli_numbers_ramanujan_congruences.sf

#!/usr/bin/ruby

# Formula due to Ramanujan for computing the nth-Bernoulli number.

# See also:
#   https://en.wikipedia.org/wiki/Bernoulli_number#Ramanujan's_congruences

func ramanujan_bernoulli_number(n) is cached {

    return 1/2 if n.is_one
    return 0   if n.is_odd

    ((n%6 == 4 ? -1/2 : 1) * (n+3)/3 - sum(1 .. (n - n%6)/6, {|k|
        binomial(n+3, n - 6*k) * __FUNC__(n - 6*k)
    })) / binomial(n+3, n)
}

for n in (0..100) {
    say "B(#{n}) = #{ramanujan_bernoulli_number(n).as_rat}"
}