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 A112517 #12 Jun 08 2024 15:50:18
%S A112517 1,0,1,0,0,1,0,-2,0,1,0,-1,-4,0,1,0,0,-2,-6,0,1,0,0,4,-3,-8,0,1,0,0,4,
%T A112517 12,-4,-10,0,1,0,0,1,12,24,-5,-12,0,1,0,0,0,-5,24,40,-6,-14,0,1,0,0,0,
%U A112517 -12,-26,40,60,-7,-16,0,1,0,0,0,-6,-48,-70,60,84,-8,-18,0,1,0,0,0,-1,-8,-120,-145,84,112,-9,-20,0,1
%N A112517 Riordan array (1, x*(1+x)*(1-x*(1+x))).
%C A112517 Riordan array product (1, x*(1+x))*(1, x*(1-x)). Row sums are A112518. Inverse is A112519.
%F A112517 Riordan array (1, x*(1-2*x^2-x^3)).
%F A112517 T(n, k) = Sum_{j=0..n} C(j, n-j)*C(k, j-k)*(-1)^(j-k).
%e A112517 Triangle begins:
%e A112517 1;
%e A112517 0, 1;
%e A112517 0, 0, 1;
%e A112517 0, -2, 0, 1;
%e A112517 0, -1, -4, 0, 1;
%e A112517 0, 0, -2, -6, 0, 1;
%e A112517 ...
%t A112517 T[n_,k_]:=SeriesCoefficient[(x(1+x)(1-x(1+x)))^k,{x,0,n}]; Table[T[n,k],{n,0,12},{k,0,n}]//Flatten (* _Stefano Spezia_, Jun 08 2024 *)
%Y A112517 Cf. A112518, A112519.
%K A112517 easy,sign,tabl
%O A112517 0,8
%A A112517 _Paul Barry_, Sep 09 2005