The differences between the differences in my table are actually zero, since each difference is 100.
If you look at the other table they are not a geometric progression. I get your point, but I don't think the differences are as big as you think.
i.e. my diffs are: 100, 100, 100, 100, ...
so my 'diffs of diffs' are 0, 0, 0, 0
the original table has diffs:
22, 22, 23, 23, 24, 25, 27, 29, 32, 36, 41, 50, 64, 95, 196
so it's 'diffs of diffs' is:
0, 1, 0, 1, 1, 2, 2, 3, 4, 5, 9, 14, 31, 101
This is more of an arithmetric progression at first, with some exponential numbers tacked on the end. The first few values are small enough to be there because of rounding.
EDIT: Removed some anaylsis that seemed a bit dodgy on reading again...