Number of Circles in a complete, directed graph

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I'm looking for the total number of circles, i.e. paths with the same starting- and endpoints but no loops inbetween in a complete, i.e. fully connected directed graph.

From Wolfram Alpha, I got a solution for an undirected, complete graph: http://mathworld.wolfram.com/CompleteGraph.html

I'd really appreciate your help.

Thanks, Chris