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Don was faster because I had my own idea on this, haha. You may like to try it out nevertheless. It works without a button. Just double-click A2. Your validation dropdowns and all other formatting will be preserved, except for that of the serial number which is set (unnecessarily) for each new row. The point is that you can control this format from the code in case you want to change it in future.
Option Explicit
Private Sub Worksheet_BeforeDoubleClick(ByVal Target As Range, Cancel As Boolean)
' 16 May 2018
' insert a blank, formatted row (with formulas) at the TopRow
Const TopRow As Long = 2 ' change as required
Const NumClm As Long = 1 ' 1 = column A
Const NumFormat As String = """DSR""0000000"
' NumFormat translates to "DSR"0000000 - change as required
Dim Trigger As Range ' the cell to double-click
Dim CopyRng As Range ' the range to copy
Dim Cl As Long ' last used column
Set Trigger = Cells(TopRow, "A") ' Trigger column = "A" (can modify)
If Target.Address = Trigger.Address Then
Cl = Cells(TopRow, Columns.Count).End(xlToLeft).Column
Set CopyRng = Trigger.Resize(1, Cl)
CopyRng.Copy
CopyRng.Insert Shift:=xlDown
Application.CutCopyMode = 0
Set CopyRng = CopyRng.Offset(-1)
' delete all constant values (keep formulas):-
With CopyRng
On Error Resume Next ' if no constants are found
.SpecialCells(xlCellTypeConstants).ClearContents
On Error GoTo 0
With .Cells(NumClm)
.NumberFormat = NumFormat ' set the number format
.Value = .Offset(1).Value + 1 ' counts from the previous entry, adding 1
.HorizontalAlignment = xlLeft
End With
.Cells(NumClm + 1).Select
Cancel = True ' cancel normal double-click response
End With
End If
End Sub
To become effective, this code must be installed in the code sheet of the worksheet on which you wish to see the action. (In VBE's Project Explorer window look for "Sheet1 (Sheet1)" - unless you changed the tab's name - and double-click to open the correct code sheet on the right.)
I designed the code to make it easy for you to read and modify. You can change the insertion point (TopRow) from 2 to 3. Move the ID number to another column than A and/or move the cell on which you double-click somewhere else. I recommend that you experiment.