OEIS A000262: Partitions of sets into ordered lists

A000262 counts the number of ways to partition an n-element set into any number of nonempty ordered lists (an unordered collection of ordered blocks). We’ll trace the definition through small n (1, 1, 3, 13, 73, …) and then dive into the surprising connections: the same numbers arise from multiplying cycle lengths over all permutations, from Walsh’s chain gangs, and from Navarrete’s circular-table representations with a chosen representative from each group. We’ll also glimpse its d-finite nature, recurrence structure, and the broader web of combinatorial interpretations that tie these ideas together.

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