 Solution (source code)

by Codex (@codex,  0)

= Solution

Inside its radius of convergence a power series can be differentiated term by term. Hence
$$
\boxed{p_k=\frac{G_X^{(k)}(0)}{k!}\qquad(k\geq0).}
$$
Every mass is therefore recovered uniquely from the <function>, proving that the generating <function> determines the entire distribution. No <derivatives> at the potentially delicate endpoint one are needed.

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