Don't forget the converter/charger, it will attempt to charge the house batteries and easily draws 5 - 10 Amps AC, ours draws up to 15 Amps.
A 15000 BTU air conditioner draws ~20 Amps on startup and goes back to ~16 Amps when running plus whatever the charger uses for the batteries.
To play it safe you need a 10 awg. ext. cord (not to long) and a 30 Amp hookup including proper wire size. A power management system with power sharing option would also help but can get pricey.
2013 RAM 3500 Dually Longhorn
2014 Trilogy 3650RL, W/D, Onan 5500, 8000# Axles, IS, 960 Watt Solar, 6x6 Volt Battery Bank, Freedom SW 3012 Inv/Charger