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 A162942 a(n) = binomial(n + 1, 2)*7^2. 1
 0, 49, 147, 294, 490, 735, 1029, 1372, 1764, 2205, 2695, 3234, 3822, 4459, 5145, 5880, 6664, 7497, 8379, 9310, 10290, 11319, 12397, 13524, 14700, 15925, 17199, 18522, 19894, 21315, 22785, 24304, 25872, 27489, 29155, 30870, 32634, 34447, 36309 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of n permutations (n>=2) of 8 objects r, s, t, u, v, z, x, y with repetition allowed, containing n-2 u's. LINKS Table of n, a(n) for n=0..38. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = A027469(n+2). - R. J. Mathar, Jul 18 2009 G.f.: -49*x / (x-1)^3. - R. J. Mathar, May 02 2014 From Amiram Eldar, Sep 04 2022: (Start) Sum_{n>=1} 1/a(n) = 2/49. Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(2*log(2)-1)/49. (End) EXAMPLE If n=2 then n-2=zero (0) u, a(1) = 49 because we have sr, tr, vr, zr, xr, yr, rs, rt, rv, rz, rx, ry, ss, st, sv, sz, sx, sy, ts, tt, tv, tz, tx, ty, vs, vt, vv, vz, vx, vy, zs, zt, zv, zz, zx, zy, xs, xt, xv, xz, xx, xy, ys, yt, yv, yz, yx, yy. If n=3 then n-2 = one (1) u, a(2) = 147 >> ssu, stu, etc.. Tf n=4 then n-2 = two (2) u, a(2) = 294 >> ssuu, stuu, ..., txuu, etc.. If n=5 then n-2 = three (3) u, a(3) = 490 >> rsuuu, stuuu, ..., rxuuu, etc.. MATHEMATICA Table[Binomial[n + 1, 2]*7^2, {n, 0, 58}] PROG (PARI) a(n)=49*binomial(n+1, 2) \\ Charles R Greathouse IV, May 02 2014 CROSSREFS Cf. A046092, A027468, A027469, A035008, A123296, A162940. Sequence in context: A098442 A088535 A045897 * A027469 A044381 A044762 Adjacent sequences: A162939 A162940 A162941 * A162943 A162944 A162945 KEYWORD nonn,easy AUTHOR Zerinvary Lajos, Jul 18 2009 STATUS approved

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Last modified May 29 22:39 EDT 2023. Contains 363044 sequences. (Running on oeis4.)