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 A140107 a(n) = binomial(n+3, 3)*7^n. 7
 1, 28, 490, 6860, 84035, 941192, 9882516, 98825160, 951192165, 8877793540, 80787921214, 719746934452, 6297785676455, 54257845827920, 461191689537320, 3874010192113488, 32202709721943369, 265198785945415980, 2165790085220897170, 17554298585474640220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS With a different offset, number of n-permutations (n=4) of 8 objects: s, t, u, v, w, z, x, y with repetition allowed, containing exactly three u's. 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 (28,-294,1372,-2401). FORMULA From R. J. Mathar, Jun 03 2009: (Start) a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4). G.f.: 1/(7*x-1)^4. (End) From Amiram Eldar, Aug 28 2022: (Start) Sum_{n>=0} 1/a(n) = 756*log(7/6) - 231/2. Sum_{n>=0} (-1)^n/a(n) = 1344*log(8/7) - 357/2. (End) MAPLE seq(binomial(n+3, 3)*7^n, n=0..26); MATHEMATICA Table[Binomial[n+3, 3]7^n, {n, 0, 20}] (* or *) LinearRecurrence[{28, -294, 1372, -2401}, {1, 28, 490, 6860}, 20] (* Harvey P. Dale, Jun 21 2016 *) PROG (Magma) [7^n* Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011 (PARI) a(n)=binomial(n+3, 3)*7^n \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Sequence in context: A223997 A263949 A240463 * A028170 A211677 A076172 Adjacent sequences: A140104 A140105 A140106 * A140108 A140109 A140110 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jun 03 2008 STATUS approved

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Last modified July 12 19:36 EDT 2024. Contains 374252 sequences. (Running on oeis4.)