cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A168298 a(n) = 1 - n^2*2^n.

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%I A168298 #22 Sep 08 2022 08:45:49
%S A168298 1,-1,-15,-71,-255,-799,-2303,-6271,-16383,-41471,-102399,-247807,
%T A168298 -589823,-1384447,-3211263,-7372799,-16777215,-37879807,-84934655,
%U A168298 -189267967,-419430399,-924844031,-2030043135,-4437573631,-9663676415,-20971519999,-45365592063
%N A168298 a(n) = 1 - n^2*2^n.
%C A168298 Numerator of 2^(-n) - n^2.
%H A168298 Colin Barker, <a href="/A168298/b168298.txt">Table of n, a(n) for n = 0..1000</a>
%H A168298 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-18,20,-8).
%F A168298 a(n)= 7*a(n-1) -18*a(n-2) +20*a(n-3) -8*a(n-4) = 1-A007758(n). - _R. J. Mathar_, Nov 24 2009
%F A168298 G.f.: -(4*x^3-10*x^2+8*x-1) / ((x-1)*(2*x-1)^3). - _Colin Barker_, Feb 10 2015
%F A168298 E.g.f.: exp(x) - 2*x*(1 + 2*x)*exp(2*x). - _G. C. Greubel_, Jul 17 2016
%t A168298 f[n_]:=2^n-n^2; Table[Numerator[f[n]],{n,0,-50,-1}]
%t A168298 LinearRecurrence[{7,-18,20,-8},{1,-1,-15,-71},30] (* _Harvey P. Dale_, May 14 2019 *)
%o A168298 (PARI) Vec(-(4*x^3-10*x^2+8*x-1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ _Colin Barker_, Feb 10 2015
%o A168298 (Magma) [1-n^2*2^n: n in [0..30]]; // _Vincenzo Librandi_, Jul 18 2016
%Y A168298 Cf. A024012
%K A168298 sign,easy
%O A168298 0,3
%A A168298 _Vladimir Joseph Stephan Orlovsky_, Nov 22 2009
%E A168298 Offset corrected, keyword:sign added, and definition simplified by _R. J. Mathar_, Nov 23 2009