A047928 a(n) = n*(n-1)^2*(n-2).
0, 12, 72, 240, 600, 1260, 2352, 4032, 6480, 9900, 14520, 20592, 28392, 38220, 50400, 65280, 83232, 104652, 129960, 159600, 194040, 233772, 279312, 331200, 390000, 456300, 530712, 613872, 706440, 809100, 922560, 1047552, 1184832
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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Magma
[ n*(n-1)^2*(n-2): n in [2..40]]; // Vincenzo Librandi, May 02 2011
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Maple
seq(floor(n^6/(n^2+1)),n=1..25); # Gary Detlefs, Feb 11 2010
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Mathematica
f[n_]:=n*(n-1)^2*(n-2); f[Range[2,60]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011 *) LinearRecurrence[{5,-10,10,-5,1},{0,12,72,240,600},40] (* or *) CoefficientList[Series[-((12 x (1+x))/(-1+x)^5),{x,0,40}],x] (* Harvey P. Dale, Jul 31 2021 *)
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PARI
a(n)=n^4 - 4*n^3 + 5*n^2 - 2*n \\ Charles R Greathouse IV, May 02 2011
Formula
a(n) = 12*A002415(n+1) = 2*A083374(n) = 4*A006011(n+1) = 6*A008911(n+1). - Zerinvary Lajos, May 09 2007
a(n) = floor((n-1)^6/((n-1)^2+1)). - Gary Detlefs, Feb 11 2010
From Amiram Eldar, Nov 05 2020: (Start)
Sum_{n>=3} 1/a(n) = 7/4 - Pi^2/6.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/12 - 3/4. (End)
G.f.: -12*x*(1+x)/(-1+x)^5. - Harvey P. Dale, Jul 31 2021
a(n) = (n-1)^4 - (n-1)^2. - Katherine E. Stange, Mar 31 2022