OEIS A000165: Double factorial of even numbers

Unpack A000165, the double factorial of even numbers (2n)!! = 2^n n!. We explore its simple definition and its surprising roles—from combinatorial pairings to the size of the automorphism group of the n-dimensional hypercube, and its appearances in higher-dimensional geometry. We also touch on connections to related transforms and other OEIS sequences, with a hint of the deeper links to come in future episodes.

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