|In F197 you have ='190'!$K$7 which will return the value from K7 on a sheet named 190.|
Another way to return the same value in F197 is to use this:
=INDIRECT("'" & ROW() - 7 & "'!$K$7")
It may be hard to see but "'" is a double-quote apostrophe double-quote and "'! is a double-quote apostrophe exclamation point.
What this will do is build the text string '190'!$K$7) which the INDIRECT function will use to return the value.
As you drag this down, the ROW() function will increment but everything else will stay the same.
Granted, this formula will not look like what you asked for, but it will return the same values and meets your criteria of not "having to manually type it".
The only other way that I can think of is to use VBA to write the formula in the cells. A fairly simple macro can do that for you but we'd need to know the exact starting and ending cells and specifically what the formulas should look like.