רעכענען

That's just the web rendition of the mark the dictionary uses to indicate an ayin that disappears in other inflected forms:
מיר רעכענען
זי רעכנט

sort of the inverse of the raised dot we use in אָפֿ·ן

I'd have thought it would be ikh rekhn (no need for the pasekh-ayin), but searching for that gives "resembles rekhen, a form of ..." instead of "a form of ..."

I'm not worried about the quasi-pasekh.

Is the first person singular איך רעכן or איך רעכען?

If you search for "rekhn" it DOES NOT say it's a form of rekhenen.

And it suggests that rekhn is similar to rekhen, a form of rekhenen, which rather ignores the "dispensible ayen".

I.e., the search is in error and misleading.

Stop! You're both right! The indexer is supposed to generate the inflected forms of each word, and in this case (and probably similar ones) it gets it wrong, and lists "rekhen" in the index instead of "rekhn". I'll fix it when I get a chance ...