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 A140802 a(n) = binomial(n+3, 3)*8^n. 9
 1, 32, 640, 10240, 143360, 1835008, 22020096, 251658240, 2768240640, 29527900160, 307090161664, 3126736191488, 31267361914880, 307863255777280, 2990671627550720, 28710447624486912, 272749252432625664, 2567051787601182720, 23959150017611038720 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n>=3) of 9 objects: r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly (3) three u's. Example: (n=4) a(1)=32 uuur, uuru, uruu, ruuu, uuus, uusu, usuu, suuu, uuut, uutu, utuu, tuuu, uuuv, uuvu, uvuu, vuuu, uuuw, uuwu, uwuu, wuuu, uuuz, uuzu, uzuu, zuuu, uuux, uuxu, uxuu, xuuu, uuuy, uuyu, uyuu, yuuu LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..400 Index entries for linear recurrences with constant coefficients, signature (32,-384,2048,-4096). FORMULA G.f.: 1/(1-8*x)^4. - Vincenzo Librandi, Oct 16 2011 With offset = 3, e.g.f.: exp(8x)*x^3/3!. - Geoffrey Critzer, Oct 03 2013 From Amiram Eldar, Aug 28 2022: (Start) Sum_{n>=0} 1/a(n) = 1176*log(8/7) - 156. Sum_{n>=0} (-1)^n/a(n) = 1944*log(9/8) - 228. (End) MAPLE seq(binomial(n+3, 3)*8^n, n=0..19); MATHEMATICA nn = 21; Drop[Range[0, nn]!CoefficientList[Series[x^3/3! Exp[8x], {x, 0, nn}], x], 3] (* Geoffrey Critzer, Oct 03 2013 *) PROG (Magma) [8^n* Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011 CROSSREFS Sequence in context: A292880 A255262 A181240 * A028204 A028190 A028202 Adjacent sequences: A140799 A140800 A140801 * A140803 A140804 A140805 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jul 15 2008 STATUS approved

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Last modified September 21 19:40 EDT 2023. Contains 365503 sequences. (Running on oeis4.)