Check out these guys:
Common Sense RC
They have some great big LiPo packs, even single packs that can pump out 90+ amps continuously. They are also very reputable from all of my reading on RC forums while I was looking for a LiPo pack for my WhiteFusion build. And for such applications, I would definitely go for a high-quality battery over saving a few bucks for a battery with any question marks.
The 35C high discharge packs can push some major current per cell, and their 15C Big Packs are, of course, very high capacity. For instance, they have an 11.1V 5Ah cell that can put out 150A continuous, and it's only 4.7x3.8x13.8cm in size. Of course it's $200, but it's available. They also have a 11.1V 8Ah cell that can do 95A continuous, but it is bigger, but also cheaper. Lots of options around.
And this can't be overstated:
Be Careful. The packs have whole other dangers besides the high currents. There's a lot of energy stored in these things, and it can come out in several dangerous ways. Charging is not trivial, either, these things are a big fire hazard. In the scale you're talking about, NOTHING is trivial, don't take a single thing for granted. I'm sure you're aware, but it can't be said too many times.
ETA: Oh, just re-read and saw you need 40A, oops, sorry about that. You don't need anywhere near the outputs I listed above, but you can see from those examples that they have a LOT of options that will satisfy your 40A needs without any trouble at all.
Common Sense RC <---This is an "8C Budget Pack", it's 11.1V 6Ah, and can do 48A continuous, at only $100. Lots of options.