Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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_