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- #!/usr/bin/ruby
- # Author: Daniel "Trizen" Șuteu
- # Date: 18 February 2018
- # https://github.com/trizen
- # A new recurrence for computing Bernoulli numbers.
- # Formula:
- # a(0) = 1
- # a(n) = Sum_{k=0..n-1} (-1)^(n+k+1) * a(k) / (n - k + 1)!
- # Which gives us the nth-Bernoulli number, B_n, as:
- # B_n = a(n) * n!
- # See also:
- # https://en.wikipedia.org/wiki/Bernoulli_number
- func a((0)) { 1 }
- func a(n) is cached {
- sum(0..^n, {|k| (-1)**(n+k+1) * a(k) / (n - k + 1)! })
- }
- for n in (0..60 `by` 2) {
- printf("B(%2d) = %50s / %s\n", n, a(n)*n! -> nude)
- }
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