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%I #22 Sep 18 2022 10:07:05
%S 0,1,80,1215,8704,40625,143856,420175,1064960,2421009,5050000,9824111,
%T 18040320,31559905,52975664,85809375,134742016,205879265,307054800,
%U 448173919,641600000,902586321,1249755760,1705630895,2297217024
%N a(n) = n^5*(n^2 + 1)/2.
%H Vincenzo Librandi, <a href="/A168364/b168364.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F G.f.: x*(1 + 72*x + 603*x^2 + 1168*x^3 + 603*x^4 + 72*x^5 + x^6)/(1-x)^8. - _Harvey P. Dale_, Apr 22 2011
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - _G. C. Greubel_, Jul 19 2016
%t Table[n^5(n^2+1)/2,{n,0,25}] (* _Harvey P. Dale_, Apr 22 2011 *)
%t LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1},{0, 1, 80, 1215, 8704, 40625, 143856, 420175}, 50] (* _G. C. Greubel_, Jul 19 2016 *)
%o (Magma) [n^5*(n^2+1)/2: n in [0..30]]; // _Vincenzo Librandi_, Aug 28 2011
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 11 2009
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