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%I #27 Sep 08 2022 08:44:49
%S 24,40,64,98,144,204,280,374,488,624,784,970,1184,1428,1704,2014,2360,
%T 2744,3168,3634,4144,4700,5304,5958,6664,7424,8240,9114,10048,11044,
%U 12104,13230,14424,15688,17024,18434,19920,21484,23128,24854,26664
%N a(n) = dot_product(1,2,...,n)*(4,5,...,n,1,2,3).
%H Vincenzo Librandi, <a href="/A026040/b026040.txt">Table of n, a(n) for n = 4..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = n(n^2 - 3n + 14)/3 (n >= 4). - _Emeric Deutsch_, Nov 27 2006
%F G.f.: x^4*(24 - 56*x + 48*x^2 - 14*x^3)/(1 - x)^4. - _Colin Barker_, Sep 17 2012
%p a:=n->n*(n^2-3*n+14)/3: seq(a(n),n=4..50); # _Emeric Deutsch_, Nov 27 2006
%t Table[Range[n].RotateLeft[Range[n],3], {n,4,52}] (* _T. D. Noe_, Nov 07 2006 *)
%t CoefficientList[Series[(24 - 56 x + 48 x^2 - 14 x^3)/(1 - x)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)
%o (Magma) [n*(n^2-3*n+14)/3: n in [4..50]]; // _Vincenzo Librandi_, Oct 17 2013
%Y Column 3 of triangle A094414.
%K nonn,easy
%O 4,1
%A _Clark Kimberling_
%E Corrected by _T. D. Noe_, Nov 07 2006
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