This is a sequence that I made. I poured by blood and sweat into this! OK, no, it was more like orange juice and yogurt. It wasn't really all that hard, I guess. It might be tricky to figure out, though! You'll know for sure when you've got it. Here's a fair warning, though, you're going to have to do some digging to confirm the 33rd term (that's the really big one).
0, 2, 1, 0, 2, 3, 0, 6, 6, 4, 44, 1, 180, 42, 16, 1096, 7652, 13781, 8,
24000, 119779, 458561, 152116956851941670912, 1054535, -53, 26, 27, 59,
4806078, 2, 35792568, 3010349, 2387010102192469724605148123694256128, 2,
0, -53, 43, 0, -4097, 173,...
I've given you the first 40 terms so there shouldn't be more than one possible answer. To help rule that out, though, I'll add this:
This is a finite list. You get an error if you try to get more than 52 terms.
"2387010102192469724605148123694256128";
128, 256 hmm.. maybe... $\endgroup$