With a different offset, number of n-permutations (n>=8) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly eight (8) u's.
If n=8 then a(0)=1.
Example: a(1)=45 because we have
uuuuuuuut, uuuuuuuuv, uuuuuuuuz, uuuuuuuux, uuuuuuuuy,
uuuuuuutu, uuuuuuuvu, uuuuuuuzu, uuuuuuuxu, uuuuuuuyu,
uuuuuutuu, uuuuuuvuu, uuuuuuzuu, uuuuuuxuu, uuuuuuyuu,
uuuuutuuu, uuuuuvuuu, uuuuuzuuu, uuuuuxuuu, uuuuuyuuu,
uuuutuuuu, uuuuvuuuu, uuuuzuuuu, uuuuxuuuu, uuuuyuuuu,
uuutuuuuu, uuuvuuuuu, uuuzuuuuu, uuuxuuuuu, uuuyuuuuu,
uutuuuuuu, uuvuuuuuu, uuzuuuuuu, uuxuuuuuu, uuyuuuuuu,
utuuuuuuu, uvuuuuuuu, uzuuuuuuu, uxuuuuuuu, uyuuuuuuu,
tuuuuuuuu, vuuuuuuuu, zuuuuuuuu, xuuuuuuuu, yuuuuuuuu.