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A140405
a(n) = binomial(n+6, 6)*5^n.
2
1, 35, 700, 10500, 131250, 1443750, 14437500, 134062500, 1173046875, 9775390625, 78203125000, 604296875000, 4532226562500, 33120117187500, 236572265625000, 1656005859375000, 11385040283203125, 77016448974609375, 513442993164062500, 3377914428710937500
OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=6) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's.
If n=6 then a(0)=1.
Example: a(1)=35 because we have
uuuuuut, uuuuutu, uuuutuu, uuutuuu, uutuuuu, utuuuuu, tuuuuuu,
uuuuuuv, uuuuuvu, uuuuvuu, uuuvuuu, uuvuuuu, uvuuuuu, vuuuuuu,
uuuuuuz, uuuuuzu, uuuuzuu, uuuzuuu, uuzuuuu, uzuuuuu, zuuuuuu,
uuuuuux, uuuuuxu, uuuuxuu, uuuxuuu, uuxuuuu, uxuuuuu, xuuuuuu,
uuuuuuy, uuuuuyu, uuuuyuu, uuuyuuu, uuyuuuu, uyuuuuu, yuuuuuu.
LINKS
FORMULA
G.f.: 1/(1-5*x)^7. - Zerinvary Lajos, Aug 06 2008
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 6856 - 30720*log(5/4).
Sum_{n>=0} (-1)^n/a(n) = 233280*log(6/5) - 42531. (End)
MAPLE
seq(binomial(n+6, 6)*5^n, n=0..18);
MATHEMATICA
Table[Binomial[n+6, 6]5^n, {n, 0, 20}] (* Harvey P. Dale, Dec 03 2017 *)
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 16 2008
STATUS
approved