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What did Rota mean by "one can define cumulants relative to any sequence of binomial type"?

.$ (E.g., the second and third cumulants are just the central moments, and the fourth cumulant is the fourth central moment minus three times the square of the variance.) … That gives us moments relative that other sequence of binomial type, and the cumulants would be related to the moments just as in lines \eqref{462420_1} and \eqref{462420_2} above. …
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