OEIS A000325: 2^n - n

A000325 is the simple formula a_n = 2^n − n, with the start 1, 1, 2, 5, 12, 27, 58. It counts all subsets of an n‑element set except the n singletons (i.e., 2^n minus n). The sequence also satisfies the recurrence a_n = 2 a_{n−1} + (n−2) with a_0 = 1, leading to the clean closed form a_n = 2^n − n. In this episode we’ll unpack the intuition, derive the formula, and explore the various combinatorial interpretations and appearances of this compact, universal counting principle.

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