I found the following code at http://www.mcgimpsey.com/excel/timestamp.html
quite useful.

The only question is that how to make it work if a series is entered if a
collection/range is changed?
e.g.
1. Selecting A2:A15, entering xyz and hitting Ctrl+Enter; OR
2. Copying xyz from some other place and pasting/filling all the range in a
single stroke?:

Private Sub Worksheet_Change(ByVal Target As Excel.Range)
With Target
If .Count 1 Then Exit Sub
If Not Intersect(Range("A:A"), .Cells) Is Nothing Then
Application.EnableEvents = False
If IsEmpty(.Value) Then
.Offset(0, 1).ClearContents
Else
With .Offset(0, 1)
.NumberFormat = "dd mmm yyyy hh:mm:ss"
.Value = Now
End With
End If
Application.EnableEvents = True
End If
End With
End Sub

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Best Regards,
FARAZ A. QURESHI