A047927 a(n) = n*(n-1)*(n-2)^2.
0, 6, 48, 180, 480, 1050, 2016, 3528, 5760, 8910, 13200, 18876, 26208, 35490, 47040, 61200, 78336, 98838, 123120, 151620, 184800, 223146, 267168, 317400, 374400, 438750, 511056, 591948, 682080, 782130, 892800, 1014816, 1148928, 1295910, 1456560, 1631700, 1822176
Offset: 2
Links
- Vincenzo Librandi, Table of n, a(n) for n = 2..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Haskell
a047927 n = if n == 2 then 0 else a245334 n 3 -- Reinhard Zumkeller, Aug 31 2014
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Magma
[n*(n-1)*(n-2)^2: n in [2..40]]; // Vincenzo Librandi, May 02 2011
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Mathematica
a[n_] := n*(n-1)*(n-2)^2; Array[a, 50, 2] (* Amiram Eldar, Jan 15 2023 *)
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PARI
a(n)=n*(n-1)*(n-2)^2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
From R. J. Mathar, May 01 2014: (Start)
G.f.: -6*x^3*(1+3*x) / (x-1)^5.
a(n) = 6*A002417(n-2). (End)
a(n) = A245334(n,3), n > 2. - Reinhard Zumkeller, Aug 31 2014
From Amiram Eldar, Jan 15 2023: (Start)
Sum_{n>=3} 1/a(n) = Pi^2/12 - 5/8.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/24 - 2*log(2) + 9/8. (End)
Extensions
Offset changed from 0 to 2 by Vincenzo Librandi, May 02 2011