I post a problem today and its solution on Thursday.
Comments are fine, though if you don't want to get a hint, don't read them.
Find the coefficient of x100 in the Taylor series for the rational function which has
x41 - x40 - x36 + x35 -x31 + x30 + x26 - x25- x16 + x15 + x11 - x10 + x6 - x5 -x+1
For better readability see my pdf file with the problem in it here
Is there a clever way to do the problem? If the way to do it was to actually do the Taylor series then
1) I wouldn't post it
2) I probably could not do it (or it would take too long to bother) though maybe there are freely available programs that could.
So yes, there is a clever solution. At least I think it's clever.