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EXAMPLE
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a(3) = 120 because 3^3 = 27 and we have [27], [8, 8, 8, 1, 1, 1] (20 permutations), [8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (78 permutations), [8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] (20 permutations), [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] and 1 + 20 + 78 + 20 + 1 = 120.
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