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
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
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jul 18 2009
STATUS
approved