= Touchard polynomials
{wiki=Touchard_polynomials}
Touchard polynomials, named after the French mathematician Jacques Touchard, are a sequence of polynomials that arise in the study of combinatorial structures, particularly in connection with the enumeration of permutations and other combinatorial configurations. These polynomials can be defined using the generating function approach for certain combinatorial objects, such as exponential generating functions for permutations with specific properties. Touchard polynomials can be expressed in several equivalent ways, including through a recursive formula or by explicit polynomial forms.
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