%I #18 Sep 08 2022 08:44:48

%S 1,4,-7,-118,-399,0,7849,61318,357857,1894076,9665625,48667074,

%T 243891793,1220331832,6102977801,30516818750,152586842049,

%U 762938033268,3814695376057,19073483852026,95367428440625

%N a(n) = 5^n - n^5.

%H Vincenzo Librandi, <a href="/A024054/b024054.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (11, -45, 95, -115, 81, -31, 5).

%F G.f.: (-6*x^6 - 123*x^5 - 319*x^4 - 44*x^3 + 6*x^2 + 7*x - 1)/((x - 1)^6*(5*x - 1)). - _Harvey P. Dale_, Oct 15 2014

%F a(0)=1, a(1)=4, a(2)=-7, a(3)=-118, a(4)=-399, a(5)=0, a(6)=7849, a(n) = 11*a(n-1) - 45*a(n-2) + 95*a(n-3) - 115*a(n-4) + 81*a(n-5) - 31*a(n-6) + 5*a(n-7). - _Harvey P. Dale_, Oct 15 2014

%t lst={}; Do[AppendTo[lst,5^n-n^5],{n,0,5!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009 *)

%t Table[5^n-n^5,{n,0,20}] (* or *) LinearRecurrence[{11,-45,95,-115,81,-31,5},{1,4,-7,-118,-399,0,7849},30] (* _Harvey P. Dale_, Oct 15 2014 *)

%o (Magma) [5^n-n^5: n in [0..30]]; // _Vincenzo Librandi_, May 14 2011

%o (PARI) a(n)=5^n-n^5 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A024012, A024026, A058794, A024040. - _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_