pascal triangle gives overflow for 13 - vb.net

Question

I wrote a code to output Pascal triangle in a multi-line textbook. The program works fine for inputs between 1 to 12 but gives an overflow error once a value of 13 is inputed.
Is there any modifications I can make to enable the program to accurately give outputs for 13 and higher?
Here is the code I used:
Public Class pascal_triangle
Private Function factorial(ByVal k As Integer) As Integer
If k = 0 Or k = 1 Then
Return 1
Else
Return k * factorial(k - 1)
End If
End Function
Private Sub BtnGen_Click(sender As Object, e As EventArgs) Handles BtnGen.Click
Dim nCr As Integer
Dim i, j, k As Integer
Dim output As String
output = ""
j = Val(TxtColumn.Text)
For k = 0 To j
For i = 0 To k
Dim fact, fact1, fact2 As Integer
fact = factorial(k)
fact1 = factorial(k - i)
fact2 = factorial(i)
nCr = fact / (fact1 * fact2)
TxtOutput.Text += Str(nCr) & output
Next
TxtOutput.Text += vbCrLf
Next
End Sub
End Class

Answer 1

The overflow is because 13! is too big to fit in an integer.
The largest representable integer (32-bit signed) is
2147483647 (0x7FFFFFFF == 01111111 11111111 11111111 11111111b)
so :
12! = 479001600
MaxInt = 2147483647
13! = 6227020800
If you want to use larger numbers than this you need to use a larger number type. The next larger types are Long (64-bit signed, max 9223372036854775807) or, for your purposes, ULong (unsigned 64-bit, since you don't need negative numbers, which is twice that at 18446744073709551615).
This will let you calculate up to20!, which is 2432902008176640000. For numbers larger than this you will need to look into using either BigInteger or other dedicated libraries that allow for holding and calculating arbitrarily large numbers.
Alternatively, you can look into other methods of computing an arbitrary row without using factorials.

Answer 2

Your main problem is that you are using Integer which is too small to hold the factorial of 13. Change your Factorial function to return Long. It would also be a good idea to turn Option Strict On and make nCr a Double.
Private Function factorial(ByVal k As Integer) As Long
If k = 0 Or k = 1 Then
Return 1
Else
Return k * factorial(k - 1)
End If
End Function
Private Sub BtnGen_Click(sender As Object, e As EventArgs) Handles BtnGen.Click
Dim nCr As Double
Dim i, j, k As Integer
Integer.TryParse(TxtColumn.Text, j)
For k = 0 To j
For i = 0 To k
Dim fact, fact1, fact2 As Long
fact = factorial(k)
fact1 = factorial(k - i)
fact2 = factorial(i)
nCr = fact / (fact1 * fact2)
TxtOutput.Text += nCr.ToString & " "
Next
TxtOutput.Text += vbCrLf
Next
End Sub