What is the coefficient of -LSB- math -RSB- x ^ n -LSB- / math -RSB- in -LSB- math -RSB- -LRB- 1 + x + 2 x ^ 2 + 3 x ^ 3 + \ dots + n x ^ n -RRB- ^ n -LSB- / math -RSB- ?
What is the value of -LSB- math -RSB- 1 ! + 2 ! + 3 ! + \ dots + 100 ! -LSB- / math -RSB- ?