Const max_N = 20, max_ciclos = 1000000

Function Factorial(Byval N As Integer) As Double
    Dim As Double d: d = 1
    If N = 0 Then Factorial = 1: Exit Function
    While (N > 1)
        d *= N
        N -= 1
    Wend
    Factorial = d
End Function

Function Analytical(N As Integer) As Double
    Dim As Double i, sum = 0
    For i = 1 To N
        sum += Factorial(N) / N^i / Factorial(N-i)
    Next i
    Return sum
End Function

Function Average(N As Integer, ciclos As Double) As Double
    Dim As Integer i, x, bits, sum = 0
    For i = 0 To ciclos - 1
        x = 1 : bits = 0
        While (bits And x) = 0
            sum += 1
            bits Or= x
            x = 1 Shl (Rnd * (N - 1))
        Wend
    Next i
    Return sum / ciclos
End Function

Randomize Timer
Print " N    promedio   analitico    (error)"
Print "--- ---------- ----------- ----------"
For N As Integer = 1 To max_N
    Dim As Double avg = Average(N, max_ciclos)
    Dim As Double ana = Analytical(N)
    Dim As Double diff = abs(avg-ana) / ana * 100
    Print Using " ## #####.###0  #####.###0    ###.#0%"; N; avg; ana; diff
Next N
Sleep