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

2,2

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).

Formula

a(n) = A002378(n)*A002378(n+1). - Zerinvary Lajos, Apr 11 2006

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

Maple

seq(floor(n^6/(n^2+1)), n=1..25); # Gary Detlefs, Feb 11 2010

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 *)

Prog

(Magma) [ n*(n-1)^2*(n-2): n in [2..40]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=n^4 - 4*n^3 + 5*n^2 - 2*n \\ Charles R Greathouse IV, May 02, 2011

Crossrefs

Cf. A002378, A002415, A006011, A008911, A083374.

Sequence in context: A304164 A199531 A188660 * A300847 A235870 A008533

Adjacent sequences: A047925 A047926 A047927 * A047929 A047930 A047931

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved