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 A248157 #19 May 16 2025 17:37:08
%S A248157 1,-2,1,0,-1,2,-3,4,-5,6,-7,8,-9,10,-11,12,-13,14,-15,16,-17,18,-19,
%T A248157 20,-21,22,-23,24,-25,26,-27,28,-29,30,-31,32,-33,34,-35,36,-37,38,
%U A248157 -39,40,-41,42,-43,44,-45,46,-47,48,-49,50,-51,52,-53,54,-55,56,-57
%N A248157 Expansion of (1 - 2*x^2)/(1 + x)^2.
%C A248157 First column of Riordan triangle A248156.
%H A248157 G. C. Greubel, <a href="/A248157/b248157.txt">Table of n, a(n) for n = 0..5000</a>
%H A248157 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-2,-1).
%F A248157 O.g.f.: (1 - 2*x^2)/(1 + x)^2 = -2 + 4/(1+x) - 1/(1+x)^2.
%F A248157 a(n) = -2*delta(n,0) + (-1)^n*(3 - n), n >= 0, with Kronecker delta(n,0) = 1 if n=0 else 0.
%F A248157 a(0) = 1, a(n) = -2*a(n-1) - a(n-2), n >= 3, with a(1) = -2, a(2) = 1.
%F A248157 a(n) = A038608(n-3) = A097141(n-1), n>=3.
%F A248157 E.g.f.: (3+x)*exp(-x) - 2. - _G. C. Greubel_, May 16 2025
%t A248157 CoefficientList[Series[(1-2x^2)/(1+x)^2,{x,0,60}],x] (* or *) LinearRecurrence[{-2,-1},{1,-2,1},60] (* _Harvey P. Dale_, Aug 25 2023 *)
%o A248157 (PARI) Vec((1 - 2*x^2)/(1 + x)^2 + O(x^80)) \\ _Michel Marcus_, Oct 11 2014
%o A248157 (Magma)
%o A248157 A248157:= func< n | n eq 0 select 1 else (-1)^n*(3-n) >; // _G. C. Greubel_, May 16 2025
%o A248157 (SageMath)
%o A248157 def A248157(n): return (-1)^n*(3-n) - 2*int(n==0) # _G. C. Greubel_, May 16 2025
%Y A248157 Cf. A038608, A097141, A248156 (row k=0).
%K A248157 sign,easy,less
%O A248157 0,2
%A A248157 _Wolfdieter Lang_, Oct 05 2014