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A162940
a(n) = binomial(n+1,2)*6^2.
1
0, 36, 108, 216, 360, 540, 756, 1008, 1296, 1620, 1980, 2376, 2808, 3276, 3780, 4320, 4896, 5508, 6156, 6840, 7560, 8316, 9108, 9936, 10800, 11700, 12636, 13608, 14616, 15660, 16740, 17856, 19008, 20196, 21420, 22680, 23976, 25308, 26676, 28080, 29520, 30996
OFFSET
0,2
COMMENTS
Number of n permutations (n>=2) of 7 objects s, t, u, v, z, x, y with repetition allowed, containing n-2 u's. Example: If n=2 then n-2 = zero (0) u, a(1)=36 because we have 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) = 108, >> ssu, stu, etc. If n=4 then n-2 = two (2) u, a(2)= 216, >> ssuu, stuu, ..., txuu, etc. If n=5 then n-2 = three (3) u, a(3)=360, >> ssuuu, stuuu, ..., txuuu, etc.
FORMULA
From Amiram Eldar, Sep 01 2022: (Start)
Sum_{n>=1} 1/a(n) = 1/18.
Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/9 - 1/18. (End)
From Amiram Eldar, Feb 22 2023: (Start)
a(n) = 18*n*(n+1) = 36*A000217(n) = 18*A002378(n).
Product_{n>=1} (1 - 1/a(n)) = -(18/Pi)*cos(sqrt(11)*Pi/6).
Product_{n>=1} (1 + 1/a(n)) = (18/Pi)*cos(sqrt(7)*Pi/6). (End)
MATHEMATICA
Table[Binomial[n + 1, 2]*6^2, {n, 0, 58}]
PROG
(PARI) a(n)=18*n*(n+1) \\ Charles R Greathouse IV, Jun 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jul 18 2009, Jul 19 2009
STATUS
approved