gistfile1.rb

#!/usr/bin/env ruby

def y(n)
  case n
    when 0 then 1
    when 1 then 0
    when 2 then -4
    when 3 then 0
    else y(n - 4)
  end
end

puts (0..(ARGV.pop or gets).to_i).map { |n| "\\frac{#{y(n)}}{#{n}!}x^{#{n}}" }.join(' + ') + "\\dots"