Is there a need for corrigendum in this case?
You don't specify your field, but in engineering and physics typos in formulae are fairly common (I daresay that papers without typos are the exception rather than the rule), and, no, there's really no need to write a corrigendum, especially if the formula is well known (everyone will understand that it's a typo).

Of course, in the above I assumed that what you derived in the rest of the paper was derived with the right formula.