%I #25 Sep 08 2022 08:44:49
%S 45,80,126,184,255,340,440,556,689,840,1010,1200,1411,1644,1900,2180,
%T 2485,2816,3174,3560,3975,4420,4896,5404,5945,6520,7130,7776,8459,
%U 9180,9940,10740,11581,12464,13390,14360,15375,16436,17544,18700,19905,21160,22466,23824,25235,26700,28220
%N a(n) = dot_product(n,n-1,...2,1)*(5,6,...,n,1,2,3,4).
%H Vincenzo Librandi, <a href="/A026060/b026060.txt">Table of n, a(n) for n = 5..10000</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 + 15*n - 46)/6. - _Ralf Stephan_, Apr 30 2004
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(5)=45, a(6)=80, a(7)=126, a(8)=184. - _Harvey P. Dale_, Nov 05 2011
%F G.f.: x^5*(45 - 100*x + 76*x^2 - 20*x^3)/(1-x)^4. - _Colin Barker_, Sep 17 2012
%t Table[n (n^2+15n-46)/6,{n,5,60}] (* or *) LinearRecurrence[{4,-6,4,-1},{45,80,126,184},60] (* _Harvey P. Dale_, Nov 05 2011 *)
%o (Magma) [n*(n^2+15*n-46)/6: n in [5..60]]; // _Vincenzo Librandi_, Nov 15 2011
%Y Column 4 of triangle A094415.
%K nonn,easy
%O 5,1
%A _Clark Kimberling_