The coefficient of  x9 in the expansion of  is 1+x1+x21+x3.....1+x100

The coefficient of x9 is the number of ways of expressing 9 as a sum of two integers and a sum of three integers⇒9=0+9=1+8=2+7=3+6=4+5.      =1+2+6=1+3+5=2+3+4