Sub test_A131407_rec() 
Dim n As Long, Result As Long 
For n = 1 To 9 
Result = A131407_rec(n) 
Debug.Print n, Result 
Next n 
End Sub 

Public Function A131407_rec(n As Long) 
' Recursive formula. 
Dim imsgbox As Integer 
Dim i As Long, j As Long, Summe As Long 
If n = 0 Then 
A131407_rec = 0 
Exit Function 
ElseIf n = 1 Then 
A131407_rec = 1 
Exit Function 
ElseIf n = 2 Then 
A131407_rec = 2 
Exit Function 
ElseIf n > 2 And n < 13 Then 
Summe = Bell(n) 
For j = 2 To n - 1 
Summe = Summe + Stirling2(n, j) * A131407_rec(j) 
Next j 
Else 
imsgbox = MsgBox("Illegal input for argument *** n *** !", vbOKOnly, "A131407_rec") 
End 
End If 
A131407_rec = Summe 
End Function 

Sub test_A131407_expl() 
Dim n As Long, Result As Long 
For n = 1 To 4 
Result = A131407_expl(n) 
Debug.Print n, Result 
Next n 
End Sub 

Public Function A131407_expl(n As Long) 
 Explicit formula. For n =1, 2, 3, 4 only! 
Dim imsgbox As Integer 
Dim e As Long, f As Long, g As Long, h As Long, Summe As Long, Summe2 As Long, Summe3 As Long, Summe4 As Long 
Dim zeile As Integer, spalte As Integer 
If n = 0 Then 
A131407_expl = 0 
Exit Function 
ElseIf n = 1 Then 
A131407_expl = 1 
Exit Function 
ElseIf n = 2 Then 
A131407_expl = 2 
Exit Function 
ElseIf n > 2 And n < 5 Then 
Summe = Bell(n) 
For e = 2 To n - 1 
Summe2 = Bell(e) 
For f = 2 To e - 1 
Summe3 = Bell(f) 
For g = 2 To f - 1 
Summe4 = Bell(g) 
For h = 2 To g - 1 
Summe4 = Summe4 + Stirling2(g, h) 
spalte = spalte + 4 
Next h 
Summe3 = Summe3 + Stirling2(f, g) * Summe4 
Next g 
Summe2 = Summe2 + Stirling2(e, f) * Summe3 
Next f 
zeile = zeile + 1 
Summe = Summe + Stirling2(n, e) * Summe2 
Next e 
Else 
imsgbox = MsgBox("Illegal input for argument *** n *** !", vbOKOnly, "A131407_expl") 
End 
End If 
A131407_expl = Summe 
End Function 

Function Bell(n As Long) 
' Berechne die Bellschen Zahlen. 
Dim imsgbox As Integer 
Dim i As Long 
If n > 2147483648# Then 
imsgbox = MsgBox("n needs to be smaller than 2147483648 !", vbOKOnly, "Bell") 
End 
End If 
If (n < 0) Then 
imsgbox = MsgBox("n needs to be greater than 0 !", vbOKOnly, "Bell") 
End 
End If 
Bell = 0 
For i = 1 To n 
Bell = Bell + Stirling2(n, i) 
Next i 
End Function 

Sub Test_Stirling2() 
Dim n As Long, k As Long, dummy As Long, dummy2 As Long 
k = 3 
For n = 1 To 10 
dummy = Stirling2(n, k) 
Debug.Print n, k, dummy 
Next n 
End Sub 

Function Stirling2(n As Long, k As Long) 
' Berechne die Stirlingschen Zahlen der zweiten Art. 
Dim i As Long, Summe As Long 
Summe = 0 
For i = 0 To k 
Summe = Summe + ((-1) ^ i) * binomial(k, i) * (k - i) ^ n 
Next i 
Stirling2 = (1 / faculty(k)) * Summe 
End Function 
Sub Test_binomial() 
Dim n As Long, dummy As Long 
n = 6 
dummy = binomial(n, 4) 
Debug.Print n, dummy 
End Sub 

Function binomial(m As Long, n As Long) 
' Berechne die Binomialzahlen. 
Dim Result As Long 
Result = faculty(m) / (faculty(m - n) * faculty(n)) 
binomial = Result 
End Function 

Function faculty(n As Long) 
' Berechne die Fakultat (ohne Rekursion). 
Dim Result As Long, i As Long 
Result = 1 
For i = 2 To n 
Result = Result * i 
Next i 
faculty = Result 
End Function