Does anyone recognize these polynomials? Need to compute a riemann lebesgue type limit

Question

These polynomials show up naturally in my work $$ p_n(x) = \sum_{j=0}^n {n \choose j} \frac{(-x)^j}{j!} $$ Does anyone know recognize if they belong to any class of well known polynomials. I am trying to compute $$ \lim_{n \rightarrow \infty} \int_{R^2} f(|r|)e^{-\frac{a}{2}|x|^2} p_n(a x) \, dx $$ for some nice function f and $a > 0$. I think the limit should be 0.

Answer 1

Maple says $$\sum _{j=0}^{n}{\frac {{n\choose j} \left( -z \right) ^{j}}{j!}}={L}_n \left(z \right)$$ Laguerre polynomials. See https://en.wikipedia.org/wiki/Laguerre_polynomials and go down to "closed form".