I know this will sound like a general question, but given the polynomial sequence $P_{n}(x)={e}^{-x}\sum_{k=0}^{\infty}\frac{a_{k}{x}^{k}}{k!}$, what are some some of its properties like recurrence relations, generating functions, is it of bynomial type, I know that when $a_{k}={k}^{n}$, we have $P_{n}(x)=T_{n}(x)=Touchard \ polynomials$.