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%I #21 Sep 08 2022 08:45:39
%S 0,-3,2,123,684,2345,6222,14007,28088,51669,88890,144947,226212,
%T 340353,496454,705135,978672,1331117,1778418,2338539,3031580,3879897,
%U 4908222,6143783,7616424,9358725,11406122,13797027,16572948,19778609,23462070
%N a(n) = n^5-n^4-n^3-n^2-n.
%H Vincenzo Librandi, <a href="/A152017/b152017.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n) = 6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6), n>5. - _Harvey P. Dale_, Sep 13 2011
%F G.f. x*(-3+20*x+66*x^2+36*x^3+x^4) / (x-1)^6. - _R. J. Mathar_, Nov 17 2011
%t lst={};Do[AppendTo[lst,n^5-n^4-n^3-n^2-n],{n,0,5!}];lst
%t Table[n^5-Total[n^Range[4]],{n,0,30}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,-3,2,123,684,2345},30](* _Harvey P. Dale_, Sep 13 2011 *)
%o (Magma) [n^5-n^4-n^3-n^2-n: n in [0..40]]; // _Vincenzo Librandi_, Nov 18 2011
%Y Cf. A152015, A152016.
%K sign,easy
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Nov 20 2008
%E Changed offset to 0 from _Bruno Berselli_, Nov 02 2011