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 A140220 a(n) = binomial(n+7, 7)*5^n. 2
 1, 40, 900, 15000, 206250, 2475000, 26812500, 268125000, 2513671875, 22343750000, 189921875000, 1553906250000, 12301757812500, 94628906250000, 709716796875000, 5204589843750000, 37407989501953125, 264056396484375000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n>=7) of 6 objects: t, u, v, z, x, y with repetition allowed, containing exactly seven (7) u's. If n=7 then a(0)=1. Example: a(1)=40 because we have uuuuuuut, uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuuy, uuuuuutu, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuuyu, uuuuutuu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuuyuu, uuuutuuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuuyuuu, uuutuuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuuyuuuu, uutuuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uuyuuuuu, utuuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, uyuuuuuu, tuuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu, yuuuuuuu. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA From Chai Wah Wu, Mar 20 2017: (Start) a(n) = 40*a(n-1) - 700*a(n-2) + 7000*a(n-3) - 43750*a(n-4) + 175000*a(n-5) - 437500*a(n-6) + 625000*a(n-7) - 390625*a(n-8) for n > 7. G.f.: 1/(1 - 5*x)^8. (End) MAPLE seq(binomial(n+7, 7)*5^n, n=0..18); MATHEMATICA Table[Binomial[n+7, 7]*5^n, {n, 0, 20}] (* Harvey P. Dale, Oct 07 2014 *) CoefficientList[Series[1 / (1 - 5 x)^8, {x, 0, 33}], x] (* Vincenzo Librandi, Feb 09 2018 *) PROG (Sage) [lucas_number2(n, 5, 0)*binomial(n, 7)/5^7 for n in range(7, 25)] # Zerinvary Lajos, Mar 12 2009 (MAGMA) [Binomial(n+7, 7)*5^n: n in [0..20]]; // Vincenzo Librandi, Feb 09 2018 CROSSREFS Sequence in context: A013346 A013348 A013349 * A130610 A279582 A004339 Adjacent sequences:  A140217 A140218 A140219 * A140221 A140222 A140223 KEYWORD nonn AUTHOR Zerinvary Lajos, Jun 23 2008 STATUS approved

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Last modified January 19 14:34 EST 2022. Contains 350466 sequences. (Running on oeis4.)