Creating the first few of these tables by hand is desirable, but after you get the hang of it, you would want to automate. That's where the CAS comes into play. If you have advanced students who know a bit of Mathematica, then you might want to simply point them in direction of basic functions that let you efficiently compute successive differences in a list. Using either RotateRight or Partition (with an offset), you can do the basic calculations in one line. Click here to see how this is done
More likely, you'll just want to give students a tool. To get a nice, neat table, it's a bit harder in Mathematica than using a spreadsheet. Click here for a Mathematica notebook that automates the operations discussed in this section.