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A140346 a(n) = binomial(n+8, 8)*5^n. 1
1, 45, 1125, 20625, 309375, 4021875, 46921875, 502734375, 5027343750, 47480468750, 427324218750, 3690527343750, 30754394531250, 248400878906250, 1951721191406250, 14963195800781250, 112223968505859375, 825176239013671875, 5959606170654296875, 42344570159912109375 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (45,-900,10500,-78750,393750,-1312500,2812500,-3515625,1953125).
FORMULA
From Chai Wah Wu, Mar 20 2017: (Start)
a(n) = 45*a(n-1) - 900*a(n-2) + 10500*a(n-3) - 78750*a(n-4) + 393750*a(n-5) - 1312500*a(n-6) + 2812500*a(n-7) - 3515625*a(n-8) + 1953125*a(n-9) for n > 8.
G.f.: 1/(1 - 5*x)^9. (End)
From Amiram Eldar, Aug 29 2022: (Start)
Sum_{n>=0} 1/a(n) = 11197440*log(6/5) - 14290736/7.
Sum_{n>=0} (-1)^n/a(n) = 3071048/21 - 655360*log(5/4). (End)
MAPLE
seq(binomial(n+8, 8)*5^n, n=0..18);
MATHEMATICA
Table[Binomial[n + 8, 8] 5^n, {n, 0, 16}] (* or *)
CoefficientList[Series[1/(1 - 5 x)^9, {x, 0, 16}], x] (* Michael De Vlieger, Mar 20 2017 *)
CROSSREFS
Sequence in context: A177728 A265615 A320363 * A268870 A049447 A327510
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 23 2008
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)