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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 (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

Table of n, a(n) for n=0..16.

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)

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 *)

PROG

(Sage)[lucas_number2(n, 5, 0)*binomial(n, 8)/5^8 for n in range(8, 25)] # Zerinvary Lajos, Mar 12 2009

CROSSREFS

Sequence in context: A177728 A265615 A320363 * A268870 A049447 A327510

Adjacent sequences:  A140343 A140344 A140345 * A140347 A140348 A140349

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, Jun 23 2008

STATUS

approved

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Last modified September 18 19:30 EDT 2021. Contains 347534 sequences. (Running on oeis4.)