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Given the formal Taylor series, or e.g.f., $f(x) = 1 + \sum_{n \geq 1} m_n \; \frac{x^n}{n!}$, the classical formal cumulants $c_n$ are generated from the formal moments $m_n$ via $ \sum_{n \geq 1} ...

On pg. 85 of The Rise and Development of Theory of Series up to the Early 1820s by Ferraro is a series soln. of $$ d^2z/z = -x^2dx^2 $$ related to the reputed first appearance of a Riccati-type eqn.,...