 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-145/2/d/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The sum is the chromatic polynomial of the path, so

\sum_{k = 1}^{n} {n k}_{P_{n}} x^{\underline{k}} = x (x - 1)^{n - 1} .

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