I'm sorry, but there seems to be no built in feature for doing this, in a similar fashion.
Your options are:
For formulas or series
Drag from the corner instead of double-clicking.
For formulas
Using fill
Select the first cell, extend selection to the end with CTRL+SHIFT+RIGHT,
then fill with CTRL+R.
Using copy/paste
Select the first cell, copy with CTRL+C, extend selection to the end with CTRL+SHIFT+RIGHT, then paste with CTRL+V.
For seires
Select the first cell, extend selection to the end with CTRL+SHIFT+RIGHT,
then use the fill menu and select series and press OK.
Optionally, you could write the function as a macro
And call it with a custom shortcut.
In the developer tab, record a macro and give it a proper name and shortcut.
Stop the recording, and edit the macro to the following:
Sub Fill()
Selection.AutoFill Destination:=Range(ActiveCell, Selection.End(xlToRight).Address), Type:=xlFillDefault
End Sub
Then instead of double-clicking the corner, you use the shortcut to fill the row instead.