"Are" is the easy answer, a rule of thumb. I think there is more to it. "Seats" is the theme of the sentence, hence "are", yet an indefinite article begs for "is". "A limited number" is the rheme of the sentence, and is inserted for a reason, hence "is", yet "number" is a quantifier, so quite reasonably attracts "are". As a spoken expression it would commonly contract to "there's", and the answer is contained therein, yet in printed form "are" is read quite comfortably. Furthermore, whether or not the subject is animate might bear relation to the verb: Liverpool is a well-supported club, but Everton are a good team, for example. I digress. The author must decide upon the theme of the sentence between "a limited number" and "seats", then insert his verb accordingly.
I mention this example to prove that the word ‘seats’ is irrelevant. It’s all about the word number, which can be plural or singular (it acts like a collective noun; e.g. group).
A group is
A group are
A number is
A number are
All are correct. Context determines the verb. It's not related to articles (a / the).