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 A123879 #12 Sep 08 2022 08:45:28
%S A123879 1,1,0,-3,-7,-7,5,32,57,33,-95,-311,-416,-11,1209,2745,2573,-2368,
%T A123879 -12943,-22015,-11007,40593,123712,157165,-14279,-498119,-1075179,
%U A123879 -934944,1090985,5220257,8476193,3535193,-17205600
%N A123879 Expansion of (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4).
%C A123879 Row sums of number triangle A123878.
%H A123879 G. C. Greubel, <a href="/A123879/b123879.txt">Table of n, a(n) for n = 0..1000</a>
%H A123879 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-5,3,-1).
%F A123879 a(n) = Sum_{k=0..n} Sum_{j=0..n} (-1)^(j-k)*C(n+j,2*j)*C(j+k,2*k).
%p A123879 seq(coeff(series((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4), x, n+1), x, n), n = 0 .. 40); # _G. C. Greubel_, Aug 08 2019
%t A123879 LinearRecurrence[{3,-5,3,-1}, {1,1,0,-3}, 40] (* _G. C. Greubel_, Aug 08 2019 *)
%o A123879 (PARI) my(x='x+O('x^40)); Vec((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)) \\ _G. C. Greubel_, Aug 08 2019
%o A123879 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4) )); // _G. C. Greubel_, Aug 08 2019
%o A123879 (Sage)
%o A123879 def A123879_list(prec):
%o A123879 P.<x> = PowerSeriesRing(ZZ, prec)
%o A123879 return P((1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4)).list()
%o A123879 A123879_list(40) # _G. C. Greubel_, Aug 08 2019
%o A123879 (GAP) a:=[1,1,0,-3];; for n in [5..40] do a[n]:=3*a[n-1]-5*a[n-2]+3*a[n-3]-a[n-4]; od; a; # _G. C. Greubel_, Aug 08 2019
%Y A123879 Cf. A123878, A123880.
%K A123879 easy,sign
%O A123879 0,4
%A A123879 _Paul Barry_, Oct 16 2006