sidef-scripts/Math/secant_numbers.sf

#!/usr/bin/ruby

# Algorithm for computing the secant numbers:
#
#   1, 1, 5, 61, 1385, 50521, 2702765, 199360981, 19391512145, 2404879675441, 370371188237525, ...
#

# Algorithm presented in the book:
#
#   Modern Computer Arithmetic
#           - by Richard P. Brent and Paul Zimmermann
#

# Minor optimization by Daniel "Trizen" Șuteu.

func secant_numbers (n) {
    var S = [1]

    for k in (1 .. n) {
        S[k] = S[k-1]*k
    }

    for k in (1 .. n), j in (k+1 .. n) {
        S[j] += ((j - k) * (j - k + 2) * S[j-1])
    }

    return S
}

say secant_numbers(10)