In [24]:
coins = [1, 2, 5, 10, 20, 50, 100, 200]

function count(n, m)
    if n < 0 || m <= 0
        return 0
    elseif n == 0
        return 1
    end
 
    return count( n, m - 1 ) + count( n - coins[m], m )
end

count(200, length(coins))


Out[24]:
73682