Create Dynamic Array Spill-down with Adjusting Cell References

I am attempting to create a dynamic array spill-down with cell references that adjust as the array spills down.

Say I place 10 in cell A1 and in A2 I enter:

=IF(ROWS($1:1)>9,"",LN(10+A1^2))

and manually copy this downwards. The A1 reference will adjust as I copy downwards. So the formula in A3 will refer to the value in A2. The formula in A4 will refer to the value in A3, etc.:

But this is manual rather than dynamic. Another manual formula that works is:

=IF(ROWS($1:1)>9,"",LN(10+INDEX(A:A,ROWS($1:1))^2))

The only way I have succeeded is to use VBA:

Public Function propr(r As Range, N As Long)
    Dim arr, i As Long
    
    If N = 1 Then
    propr = Application.WorksheetFunction.Ln(10# + r.Value ^ 2)
         Exit Function
    End If
    
    ReDim arr(1 To N, 1 To 1)
    arr(1, 1) = Application.WorksheetFunction.Ln(10# + r.Value ^ 2)
    For i = 2 To N
        arr(i, 1) = Application.WorksheetFunction.Ln(10# + arr(i - 1, 1) ^ 2)
    Next i
    propr = arr
End Function

But I want a formula rather than a UDF.

What I have tried:

=LN(10+INDEX(A:A,SEQUENCE(9))^2)

This generates a circular reference warning:

This should be really easy, but I am not seeing it.