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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 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.)