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.
%I A142585 #16 Apr 14 2021 22:26:37
%S A142585 1,0,1,0,-1,5,-14,35,-81,180,-389,825,-1726,3575,-7349,15020,-30561,
%T A142585 61965,-125294,252795,-509161,1024100,-2057549,4130225,-8284926,
%U A142585 16609455,-33282989,66669660,-133507081,267285605,-535010414,1070731475,-2142612801,4287086100
%N A142585 Inverse binomial transform of A014217.
%H A142585 G. C. Greubel, <a href="/A142585/b142585.txt">Table of n, a(n) for n = 0..1000</a>
%H A142585 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-3,-1,2).
%F A142585 a(n) = (-1)^(n+1) * A027974(n-4) for n > 4.
%F A142585 G.f.: (1+3*x+2*x^2+x^3)/((1+2*x)*(1+x-x^2)). - _R. J. Mathar_, Sep 22 2008
%F A142585 a(n) = (-1)^(n+1)*(2^(n-1) -F(n+1) -F(n-1)), where F(n) = A000045(n), for n>=1, with a(0)=1. - _Johannes W. Meijer_, Aug 15 2010
%F A142585 a(n) = -3*a(n-1) - a(n-2) + 2*a(n-3). - _Wesley Ivan Hurt_, Oct 06 2017
%t A142585 Table[(-1)^n*(LucasL[n] -2^(n-1)) - Boole[n==0]/2, {n,0,40}] (* _G. C. Greubel_, Apr 14 2021 *)
%o A142585 (Magma) [1] cat [(-1)^n*( Lucas(n) - 2^(n-1) ): n in [1..40]]; // _G. C. Greubel_, Apr 14 2021
%o A142585 (Sage) [1]+[(-1)^n*( lucas_number2(n,1,-1) - 2^(n-1) ) for n in (1..40)] # _G. C. Greubel_, Apr 14 2021
%Y A142585 Cf. A000032, A000045, A014217, A027974.
%K A142585 sign,easy
%O A142585 0,6
%A A142585 _Paul Curtz_, Sep 21 2008
%E A142585 Edited and extended by _R. J. Mathar_, Sep 22 2008