Solution

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{title2=$G_X(s)=\mathbb E[s^X]$}
{wiki}

= PGF
{c}
{synonym}

For a nonnegative integer-valued <random variable> $X$, its probability generating function is
$$
G_X(s)=\mathbb E[s^X]=\sum_{n\geq0}\mathbb P(X=n)s^n.
$$
The generating function of a sum of <independent random variables> is the product of their generating functions.

Probability generating function

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 Incoming links: Probability generating function