OEIS A00138: Permutations with no 4-cycles

In this episode we explore OEIS A00138—the number of permutations of n elements whose cycle decompositions contain no 4-cycles. We unpack the inclusion-exclusion formula that counts these permutations, see how the 4-cycle restriction connects to a generating function tied to the exponential series, and discuss the resulting asymptotic growth. We also peek at the surprising link to the alternating group inside the symmetric group, and walk through the concrete n=4 case (there are 18 such permutations) to illustrate the idea.

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