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The ordinary factorial may be written in terms of the Stirling numbers of thesecond kind as shown by Quaintance and Gould and the odd double factorial interms of the Stirling numbers of the first kind as shown by Callan. During thepreparation of an expository paper on Wolstenholme's Theorem, we discovered anexpression for the odd double factorial using the Stirling numbers of thesecond kind. This appears to be the first such identity involving both positiveand negative integers and the result is outlined here.

An identity for the odd double factorial