Max number of clients than can be connected to an AP ?

The user guide does not say. Found Here: http://downloads.linksys.com/downloads/userguide/WAP300N_UG_EN_3425-01640A_Web,0.pdf

That being said, normally I would not expect more than 15-30 clients for low to moderate use and maybe as low as 5 for high usage (streaming videos) before quality is affected.

I have seen a Netgear Dual-Band support 40+ users and I have seen the same support 10 users.  It all depends on what the users are doing.  You may be able to email or call support and ask, but I do not see a place where there is a hard limit.  Cisco as a rule I believe generally recommends 20-25 per antennae as the max number of users to get reasonable performance.

So if there is no hardware limit, then the answer is that the max number of clients depends on the usage scenario.

Hope this helps a bit.

It's nowhere described. That's actually how they want it, keep it in the consumer space, so that these specs aren't that important.
Therefore you should just assume 10 or 20 devices shouldn't be a problem (assuming half of those are low usage, like idle printers and stuff), but with 30+ you might experience some performance or stability issues.
Just something I estimated from the top of my head. As these are consumer/home products, even Cisco/Linksys probably didn't test it that thoroughly.