Finding the Pattern of Triangular Set of Numbers

[isthereaspoon]

I have encountered such a triangular set of numbers:

1
-8 -7
28 -16 9
-56 -65 -22 -7
70 112 51 4 1

Apart from the obvious first column being (x-1)^8, what can you find for other columns?

 

[CRGreathouse]

I can't see anything. Sloane's suggests
http://oeis.org/classic/A130595
which is tantalizing but I can't find the other parts.

 

[isthereaspoon]

thanks, it is simply hard.

 

[squelchy451]

The 'hypothenuse' seems to play a role in that

1
-8 -7
28 -16 9

-7 - 1 = -8
-7 - 9 = -16

As far as the other numbers go I haven't gotten them yet, but just putting this out there as a possible stepping stone