Counting permutations with roots

This article discusses the mathematical problem of counting permutations of n elements that have a kth root, using exponential generating functions. The author details implementing the generating function product in Mathematica and SymPy, including code snippets and output tables for various k values. The post covers technical aspects of series coefficients, truncation for efficiency, and verification against known results from Wilf's work. It is a technical tutorial focused on combinatorial mathematics and symbolic computation, relevant to IT/TECHNOLOGY as it involves programming and mathematical algorithms.