Cant count integer partitions by recursive function.

Hi guys I want to calculate the number of integer partitions. So that I use this code

Function p(m As Integer, n As Integer)
If m = 1 Or n = 1 Then
p(m, n) = 1
Else
If n > m Then
p(m, n) = p(m, m)
Else
If m = n Then
p(m, n) = p(m, m - 1) + 1
Else
p(m, n) = p(m, n - 1) + p(m - n, n)
End If
End If
End If
End Function
Sub Integer_partitions()
Debug.Print p(5, 5)
End Sub

But I get the error as " Run time error 28 Out of stuck space".
What's wrong with my code?
Regards,
Alex

Administrative Note:

We would very much like to help you with your query, however the thread title does not really convey what your request is about.

Please take a moment to amend your thread title. Make sure that the title properly explains your request. Your title should be explicit and not be generic (this includes function names used without an indication of what you are trying to achieve).

Please see Forum Rule #1 about proper thread titles and adjust accordingly. To edit the thread title, open the original post to edit and then click on Go Advanced (bottom right) to access the area where you can edit your title.

(Note: this change is not optional. No help to be offered until this moderation request has been fulfilled.)

I don't have Excel handy to test with, but my guess is that you are getting a lot of recursive calls to the function from within the function with no control over that recursion. Eventually you run out of stack space. The recursion is caused by using p as both your function name and an array variable within the function. It appears to me that the recursion is not intended or essential to the procedure, so I would write it to avoid the unintentional recursion, by changing either the name of the function or the name of the array variable. Since p is not very descriptive of the function's purpose, I would probably change the function name:

Function pwhatever(m as long, n as long) as variant
dim p(1 to 20, 1 to 20) as long 'or whatever the array dimensions need to be
'code to process the values into p
'at the end, assign the final result to the function name
pwhatever=p
end function

Function Stirling2nd(n As Long, k As Long) As Double
  ' shg 2019

  ' Returns the Stirling Number of the Second Kind* using the recurrence relation 
  ' at http://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html
  '   S(0, 0) = 1
  '   S(n, 0) = S(0, n) = 0 for n > 0
  '   Then S(n, k) = S(n - 1, k - 1) + k * S(n - 1, k)

  ' * the total number of ways to partition n labeled items into k non-empty subsets
  ' https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind

  Dim i             As Long
  Dim j             As Long
  Dim adS()         As Double

  If n < 0 Or k < 0 Or k > n Then
    Stirling2nd = 0#

  Else
    ReDim adS(0 To n, 0 To k)
    adS(0, 0) = 1#

    For i = 1 To n
      For j = 1 To IIf(k <= i, k, i)
        adS(i, j) = adS(i - 1, j - 1) + j * adS(i - 1, j)
      Next j
    Next i

    Stirling2nd = adS(n, k)
  End If
End Function

E.g,

	A	B	C	D	E	F	G	H	I	J	K	L	M	N
1	n \ k	0	1	2	3	4	5	6	7	8	9	10
2	0	1	0	0	0	0	0	0	0	0	0	0		C2: =Stirling2nd(n, k)
3	1	0	1	0	0	0	0	0	0	0	0	0
4	2	0	1	1	0	0	0	0	0	0	0	0
5	3	0	1	3	1	0	0	0	0	0	0	0
6	4	0	1	7	6	1	0	0	0	0	0	0
7	5	0	1	15	25	10	1	0	0	0	0	0
8	6	0	1	31	90	65	15	1	0	0	0	0
9	7	0	1	63	301	350	140	21	1	0	0	0
10	8	0	1	127	966	1,701	1,050	266	28	1	0	0
11	9	0	1	255	3,025	7,770	6,951	2,646	462	36	1	0
12	10	0	1	511	9,330	34,105	42,525	22,827	5,880	750	45	1