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In combinatorial mathematics, the Stirling transform of a sequence { an : n = 1, 2, 3,... } of numbers is the sequence { bn : n = 1, 2, 3,... } given by
where { n k } {\displaystyle \left\{{\begin{matrix}n\\k\end{matrix}}\right\}} is the Stirling number of the second kind, also denoted S , which is the number of partitions of a set of size n into k parts.
The inverse transform is
where s is a Stirling number of the first kind.
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