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$a_{-i}=0$ for all positive i. We have the recurrence

$ a_n = \sum_{i=1}^\infty b_ia_{n-m_i} $

Where $m_i>0$ for all $i$.

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    $b_i$ and $m_i$ are two infinite sequences. As far as I know, partition numbers can be expressed in this way.2011-12-02

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In signal processing, this is a kind of on IIR filter or in stochastics this is similar to an auto regressive process.