# Happy New Year!... and polynomials

Algebra Level 5

Define the 2015 polynomials

$$P_{n}(x)=(x-1)(x-2)...(x-n)$$

for $$n=1, 2, ..., 2015$$.

Each of these can be written as a polynomial in $$x-2016$$, with a constant term of $$Q_{n}$$. For example, $$Q_{1}=2015$$ because $$P_{1}(x)=(x-2016)+2015$$.

Find the smallest integer larger than $$\displaystyle \sum_{n=1}^{2015} \frac {Q_{n}}{2015!}$$.

×