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%I #21 Aug 25 2023 19:01:06
%S 1,-1,17,199,929,2951,7489,16367,32129,58159,98801,159479,246817,
%T 368759,534689,755551,1043969,1414367,1883089,2468519,3191201,4073959,
%U 5142017,6423119,7947649,9748751,11862449,14327767,17186849,20485079,24271201
%N a(n) = n^5 - n^3 - 2*n^2 + 1.
%H Vincenzo Librandi, <a href="/A177075/b177075.txt">Table of n, a(n) for n = 0..1000</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 G.f.: (1 - 7 x + 38 x^2 + 62 x^3 + 25 x^4 + x^5)/(1 - x)^6. - _Vincenzo Librandi_, May 03 2014
%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) for n>5.
%t CoefficientList[Series[(1 - 7 x + 38 x^2 + 62 x^3 + 25 x^4 + x^5)/(1 - x)^6, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 03 2014 *)
%t Table[n^5-n^3-2n^2+1,{n,0,50}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1,-1,17,199,929,2951},50] (* _Harvey P. Dale_, Aug 25 2023 *)
%o (PARI) a(n)=n^5-n^3-2*n^2+1 \\ _Charles R Greathouse IV_, Jan 11 2012
%o (Magma) [n^5-n^3-2*n^2+1: n in [0..40]]; // _Vincenzo Librandi_, May 03 2014
%K sign,easy
%O 0,3
%A _Vincenzo Librandi_, Jun 05 2010
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