Euler transform of a sequence
= Euler transform of a sequence
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= Euler transform
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The Euler transform of a sequence $(b_n)_{n\ge1}$ has coefficients $a_n$ defined by $\sum_{n\ge0}a_nx^n=\prod_{n\ge1}(1-x^n)^{-b_n}$. In unlabelled counting, $b_n$ may count connected components of size $n$, while $a_n$ counts <multisets> of components.