Hello, OliverQ!
Note: Everything here is, of course, my opinion.
I got tired of writing "I think ... ", "It seems that ... ", "The pattern might be ..."
If you want a function for the term,
. . I've made only a little progress.
I found some patterns among consecutive terms, but not all of them.
. .
. .
The numerators have the sum and difference of two integers:
. .
The exponents seem to be triangular numbers: 0, 1, 3, 6, . . .
The denominators are powers-of-2:
. .
The exponents are of the form: .
Now what is generating those -values? .