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 A124744 #14 Aug 27 2024 09:16:33
%S A124744 1,0,1,0,0,1,0,0,-1,1,0,0,0,-1,1,0,0,0,0,-2,1,0,0,0,0,1,-2,1,0,0,0,0,
%T A124744 0,1,-3,1,0,0,0,0,0,0,3,-3,1,0,0,0,0,0,0,-1,3,-4,1,0,0,0,0,0,0,0,-1,6,
%U A124744 -4,1,0,0,0,0,0,0,0,0,-4,6,-5,1,0,0,0,0,0,0,0,0,1,-4,10,-5,1
%N A124744 Expansion of (1+x*y)/(1-x^2*y^2+x^3*y^2).
%H A124744 Paolo Xausa, <a href="/A124744/b124744.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
%F A124744 T(n,k) = binomial(floor(k/2),n-k)*(-1)^(n-k)
%F A124744 Column k has g.f. x^k*(1-x)^floor(k/2). - _Paul Barry_, Feb 01 2007
%e A124744 Triangle begins
%e A124744 1,
%e A124744 0, 1,
%e A124744 0, 0, 1,
%e A124744 0, 0, -1, 1,
%e A124744 0, 0, 0, -1, 1,
%e A124744 0, 0, 0, 0, -2, 1,
%e A124744 0, 0, 0, 0, 1, -2, 1,
%e A124744 0, 0, 0, 0, 0, 1, -3, 1,
%e A124744 0, 0, 0, 0, 0, 0, 3, -3, 1,
%e A124744 0, 0, 0, 0, 0, 0, -1, 3, -4, 1,
%e A124744 0, 0, 0, 0, 0, 0, 0, -1, 6, -4, 1
%t A124744 Table[(-1)^(n-k)*Binomial[Floor[k/2], n-k], {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Aug 27 2024 *)
%Y A124744 Cf. A124745 (row sums), A124746 (diagonal sums), A124747 (inverse).
%K A124744 easy,sign,tabl
%O A124744 0,20
%A A124744 _Paul Barry_, Nov 06 2006