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%I #23 Sep 08 2022 08:44:49
%S 45,67,98,140,195,265,352,458,585,735,910,1112,1343,1605,1900,2230,
%T 2597,3003,3450,3940,4475,5057,5688,6370,7105,7895,8742,9648,10615,
%U 11645,12740,13902,15133,16435,17810,19260,20787,22393,24080,25850,27705
%N a(n) = dot_product(1,2,...,n)*(5,6,...,n,1,2,3,4).
%H Vincenzo Librandi, <a href="/A026043/b026043.txt">Table of n, a(n) for n = 5..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(2n^2 - 9n + 49)/6 (n >= 5). - _Emeric Deutsch_, Nov 29 2006
%F G.f.: x^5*(45 - 113*x + 100*x^2 - 30*x^3)/(1 - x)^4. - _Colin Barker_, Sep 17 2012
%p a:=n->n*(2*n^2-9*n+49)/6: seq(a(n),n=5..45); # _Emeric Deutsch_, Nov 29 2006
%t Table[Range[n].RotateLeft[Range[n],4], {n,5,51}] (* _T. D. Noe_, Nov 07 2006 *)
%t CoefficientList[Series[(45 - 113 x + 100 x^2 - 30 x^3)/(1 - x)^4, {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)
%o (Magma) [n*(2*n^2-9*n+49)/6: n in [5..60]]; // _Vincenzo Librandi_, Oct 17 2013
%Y Column 4 of triangle A094414.
%K nonn,easy
%O 5,1
%A _Clark Kimberling_
%E Corrected by _T. D. Noe_, Nov 07 2006
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