Ya, your best information is probably contacting the manufacture (they know their
nutrients best). But I will give you my reasoning behind my point. First the smaller the plant the less nutrients it needs. In fact it dosen't need any nutrients at all until it has it's first set of true leaves. Once it has the first set of true leaves it still dosen't have a need for more than a very dilute
nutrient solution (about 1/4 strength).
That's why I think that nutrient calculator is starting form mid size seedlings (not
seeds/sprouts). Going by the calculator if week one is "seeds/sprouts" 1/4 strength is 5.5 ml of both. That would make full strength 22 mL. Even if they were going by 1/3 strength that would make full strength 16.5 mL each. But that's not even close.
If you look at week 7 (almost 2 months) when the plants should be using full strength nutrient solution for well over a month at that point. The recommended mix is only 8.5 ml. So if 8.5 ml is full strength, 1/4 strength would be about 2 mL. And 1/3 strength would be just under 3 mL (5.5-6 is double that). Not that the plants wont grow (though they may suffer), but it's a big waist of nutrients at that point.
P.S.
Also people rarely if ever start seeds in the main system. They usually start seedlings in a different seedling system, or prorogation trays until their big enough to place in the main system. Witch is another reason why I'm sure the week one is not meaning starting from seeds, but rather seedlings a few inches tall instead. Also with sprouts that small, there is no reason to change the nutrient solution in a system each week. The plants are too small to use much of the nutrients at all. So it dosen't go out of balance anywhere near as fast. 27 gallons of nutrient solution should be able to support 27 lettuce plants for at least 3 weeks (probably 4 weeks) even when full grown. 27 gallons should be able to support somewhere in the neighborhood of 100 to 200 seedlings each week with no problem. Sprouts to harvest is generally about 6 weeks (8 max) for lettuce.