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 A115952 #9 Sep 08 2022 08:45:24
%S A115952 1,-1,1,-1,0,1,0,0,-1,1,0,-1,0,0,1,0,0,0,0,-1,1,0,0,-1,0,0,0,1,0,0,0,
%T A115952 0,0,0,-1,1,0,0,0,-1,0,0,0,0,1,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,-1,0,0,0,
%U A115952 0,0,1,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,0,0,0,0,-1
%N A115952 Expansion of (1-x+x*y)/(1-x^2*y^2) - x^2/(1-x^2*y).
%C A115952 Row sums are A000007. Diagonal sums are A115953. Inverse is A115954.
%H A115952 G. C. Greubel, <a href="/A115952/b115952.txt">Rows n = 0..100 of triangle, flattened</a>
%F A115952 Number triangle T(n,k)=if(n=k,1,0) OR if(n=2k+2,-1,0) OR if(n=k+1,-(1+(-1)^k)/2,0).
%e A115952 Triangle begins
%e A115952 1,
%e A115952 -1, 1,
%e A115952 -1, 0, 1,
%e A115952 0, 0, -1, 1,
%e A115952 0, -1, 0, 0, 1,
%e A115952 0, 0, 0, 0, -1, 1,
%e A115952 0, 0, -1, 0, 0, 0, 1,
%e A115952 0, 0, 0, 0, 0, 0, -1, 1,
%e A115952 0, 0, 0, -1, 0, 0, 0, 0, 1,
%e A115952 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
%e A115952 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1,
%e A115952 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
%e A115952 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1,
%e A115952 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
%e A115952 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1,
%e A115952 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1
%t A115952 T[n_, k_]:= If[n==k, 1, If[n==k+1, -(1+(-1)^k)/2, If[n==2*k+2, -1, 0]]];
%t A115952 Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* _G. C. Greubel_, May 06 2019 *)
%o A115952 (PARI) {T(n,k) = if(n==k, 1, if(n==k+1, -(1+(-1)^k)/2, if(n==2*k+2, -1, 0)))}; \\ _G. C. Greubel_, May 06 2019
%o A115952 (Magma) [[n eq k select 1 else n eq k+1 select -(1+(-1)^k)/2 else n eq 2*(k+1) select -1 else 0: k in [0..n]]: n in [0..15]]; // _G. C. Greubel_, May 06 2019
%o A115952 (Sage)
%o A115952 def T(n, k):
%o A115952 if (n==k): return 1
%o A115952 elif (n==k+1): return -(1+(-1)^k)/2
%o A115952 elif (n==2*(k+1)): return -1
%o A115952 else: return 0
%o A115952 [[T(n, k) for k in (0..n)] for n in (0..15)] # _G. C. Greubel_, May 06 2019
%Y A115952 Cf. A115524.
%K A115952 easy,sign,tabl
%O A115952 0,1
%A A115952 _Paul Barry_, Feb 02 2006