Asus X401A Recovery DVD using AI Recovery Burner
The recovery CD for the Asus X401A is not one CD. It is five DVDs!
Update: after writing the above, I discovered the Microsoft Windows 7 "make a Repair Disc" function, which creates just one CD. This allows you to recover the machine from the recovery partition.
Update II: if you wreck the UEFI boot options (like EasyBCD did for me) then the single recovery CD will not help you. It will cheerfully over-write your Windows partitions but you still won't be able to boot the machine. To do that, you'll need the full 5 DVDs, and then you'll be glad you made them, like I was.