Actuarial polynomials

This article may be very hard to understand. Please help clarify it. (October 2017)

In mathematics, the actuarial polynomials a^(β)
_n(x) are polynomials given by the generating function

${\displaystyle \displaystyle \sum _{n}{\frac {a_{n}^{(\beta )}(x)}{n!}}t^{n}=\exp(\beta t+x(1-e^{t}))}$

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