Don't forget about both the nominal rating (rather than peak) and altitude.
Your 2000W generator isn't really a 2000W generator. It's actually a 1600W generator that can do peaks up to 2000W for a few seconds or minutes (depending on the version of generator). For starting the A/C, it's good to consider peak. For sizing a generator to the other loads and constant draw of the A/C, you need to think about the nominal rating of 1600W --> 13.33 amps available (P=VI).
The next is altitude. I'm not sure where you're at, but normally aspirated engines will lose about 3% of power per 1,000' over nominal, and nominal is usually 500'. So, if you're at 2,500', then you will lose 6% and your 2000W generator is down to a 1500W generator.
Where I'm at, camping at 10,500, I'm losing around 30% of my engine's power!
A 15.5K BTU A/C is probably going to draw between 15-20 amps on startup. If you're at altitude, you probably can do this without tripping the generator. If you're higher than that, then it becomes a roll of the dice. Probably need more power or a soft-start or both.
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