%I #19 Sep 08 2022 08:44:49

%S 119,156,204,265,341,434,546,679,835,1016,1224,1461,1729,2030,2366,

%T 2739,3151,3604,4100,4641,5229,5866,6554,7295,8091,8944,9856,10829,

%U 11865,12966,14134,15371,16679,18060,19516,21049,22661,24354,26130,27991,29939,31976,34104,36325,38641,41054

%N a(n) = dot_product(1,2,...,n)*(7,8,...,n,1,2,3,4,5,6).

%H Vincenzo Librandi, <a href="/A026049/b026049.txt">Table of n, a(n) for n = 7..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^2-15n+109)/6. - _Ralf Stephan_, Apr 30 2004

%F G.f.: x^7*(119-320*x+294*x^2-91*x^3)/(1-x)^4. - _Colin Barker_, Sep 17 2012

%t CoefficientList[Series[(119 - 320 x + 294 x^2 - 91 x^3)/(1 - x)^4, {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 17 2013 *)

%o (Magma) [n*(2*n^2-15*n+109)/6: n in [7..60]]; // _Vincenzo Librandi_, Oct 17 2013

%Y Column 6 of triangle A094414.

%K nonn,easy

%O 7,1

%A _Clark Kimberling_