Полином с целыми коэффициентами.

[Руст]

Let $E_n(t)$ the Eulerian polynomial defined by:

$$\sum_{k=0}^{\infty}(k+1)^nt^k=\frac{E_n(t)}{(1-t)^{n+1}}$$

and let $B_n$ be the nth Bernoulli number. Show that

$$\left(E_{n+1}(t)-(1-t)^n\right)B_n$$

is a polynomial with integer coefficients.