In this contribution we consider the sequence ${Q_{n}^{lambda}}_{ngeq 0} $ of monic polynomials orthogonal with respect to the following inner product involving differences begin{equation*} langle p,qrangle _{lambda}=int_{0}^{infty}pleft(xright) qleft(xright) dpsi ^{(a)}(x)+lambda ,Delta p(c)Delta q(c), end{equation*} where $lambda in mathbb{R}_{+}$, $Delta $ denotes the forward difference operator defined by $Delta fleft(xright) =fleft(x+1right) -fleft(xright) $, $psi ^{(a)}$ with $a>0$ is the well known Poisson distribution of probability theory% begin{equation*} dpsi ^{(a)}(x)=frac{e^{-a}a^{x}}{x!}quad text{at}x=0,1,2,ldots, end{equation*}% and $cin mathbb{R}$ is such that $psi ^{(a)}$ has no points of increase in the interval $(c,c+1)$. We derive its corresponding hypergeometric representation. The ladder operators and two differe
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