A015242 - OEIS

%I #21 Sep 08 2022 08:44:39

%S 0,-5,-12,-9,16,75,180,343,576,891,1300,1815,2448,3211,4116,5175,6400,

%T 7803,9396,11191,13200,15435,17908,20631,23616,26875,30420,34263,

%U 38416,42891,47700,52855,58368,64251

%N a(n) = (2*n - 7)*n^2.

%H Vincenzo Librandi, <a href="/A015242/b015242.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F G.f.: x*(-5 + 8*x + 9*x^2) / (x-1)^4. - _R. J. Mathar_, Oct 25 2011

%F From _G. C. Greubel_, Jul 30 2016: (Start)

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F E.g.f.: x*(-5 - x + 2*x^2)*exp(x). (End)

%t Table[(2*n - 7)*n^2, {n,0,25}] (* or *) LinearRecurrence[{4,-6,4,-1},{0, -5, -12, -9},25] (* _G. C. Greubel_, Jul 30 2016 *)

%o (Magma) [(2*n-7)*n^2: n in [0..40]]; // _Vincenzo Librandi_, Oct 26 2011

%o (PARI) a(n)=(2*n-7)*n^2 \\ _Charles R Greathouse IV_, Jul 30 2016

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 11 1999