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EXAMPLE
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a(0) = 1: the empty word.
a(1) = 5040: abcdefg, abcdegf, abcdfeg, ..., gfedbca, gfedcab, gfedcba, (all permutations of 7 letters).
a(2) = 135135: aabbccddeeffgg, aabbccddeefgfg, aabbccddeegffg], ..., gfedcaabbcdefg, gfedcababcdefg, gfedcbaabcdefg.
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