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COMMENTS
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With a different offset, number of n-permutations (n>=7) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly seven (7) u's.
If n=7 then a(0)=1.
Example: a(1)=40 because we have
uuuuuuut, uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuuy,
uuuuuutu, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuuyu,
uuuuutuu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuuyuu,
uuuutuuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuuyuuu,
uuutuuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuuyuuuu,
uutuuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uuyuuuuu,
utuuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, uyuuuuuu,
tuuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu, yuuuuuuu.
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