login
a(n) = 1 - n^5.
5

%I #21 Sep 08 2022 08:44:48

%S 1,0,-31,-242,-1023,-3124,-7775,-16806,-32767,-59048,-99999,-161050,

%T -248831,-371292,-537823,-759374,-1048575,-1419856,-1889567,-2476098,

%U -3199999,-4084100,-5153631,-6436342,-7962623,-9765624,-11881375,-14348906,-17210367,-20511148

%N a(n) = 1 - n^5.

%H Vincenzo Librandi, <a href="/A024003/b024003.txt">Table of n, a(n) for n = 0..555</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 From _G. C. Greubel_, May 11 2017: (Start)

%F G.f.: (1 - 6*x - 16*x^2 - 76*x^3 - 21*x^4 - 2*x^5)/(1 - x)^6.

%F E.g.f.: (1 - x - 15*x^2 - 25*x^3 - 10*x^4 - x^5)*exp(x). (End)

%t 1-Range[0,50]^5 (* _Vladimir Joseph Stephan Orlovsky_, Feb 20 2011 *)

%t CoefficientList[Series[(1-6*x-16*x^2-76*x^3-21*x^4-2*x^5)/(1-x)^6, {x, 0, 50}], x] (* _G. C. Greubel_, May 11 2017 *)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,0,-31,-242,-1023,-3124},30] (* _Harvey P. Dale_, May 18 2019 *)

%o (Magma) [1-n^5: n in [0..50]]; // _Vincenzo Librandi_, Apr 29 2011

%o (PARI) x='x+O('x^50); Vec((1-6*x-16*x^2-76*x^3-21*x^4-2*x^5)/(1-x)^6) \\ _G. C. Greubel_, May 11 2017

%Y Cf. A024049.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_

%E More terms from _Harvey P. Dale_, Feb 22 2016