Interesting - and one obvious question is: how does BLP for Pantheon trinkets work?
It could be that someone at Blizzard decided that: first time it should be 17%, next time 18%, and 8th time 100% - but I doubt that.
The simplest idea would be that each week without trinket increased the chance by x% after some weeks. So roughly 10% more each week starting the fourth week, going from 17% to 27% then to 37%, 47%, 57% (all within the margin of error) - but that is clearly wrong the 8th week. It is also fails to explain why the chance increased slightly already the 3rd week.
After some failed attempts I found a fairly simple formula that almost fits the data - the root of 8th time is the charm!
The chance each week would be max(17%, 100%*(1-root(1-week/8))), with percentages 17%, 17%, 21%, 29%, 39%, 50%, 65%, 100%. It does not seem to be the exact formula, but it may be close to it.
It is not as odd as it may look - since the probability (not percentage) of not getting the trinket, i.e. the bad luck, would be: min(0.83, root(1-week/8)). That looks as something a programmer might add to do "bad luck protection".