A combinatorial survey of identities for the double factorial

TL;DR

This paper reviews combinatorial interpretations of various identities involving the double factorial, primarily using bijective methods to deepen understanding of these mathematical relationships.

Contribution

It provides a comprehensive survey of combinatorial interpretations for double factorial identities, highlighting bijective proof techniques.

Findings

Identifies multiple combinatorial interpretations of double factorial identities.

Uses bijective methods to prove and explain these identities.

Enhances understanding of double factorials through combinatorial perspectives.

Abstract

We survey combinatorial interpretations of some dozen identities for the double factorial such as, for instance, (2n-2)!! + Sum_{k=2}^{n} (2n-1)!!(2k-4)!!/(2k-1)!! = (2n-1)!!. Our methods are mostly bijective.