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 A165620 #12 Jul 16 2019 03:41:02
%S A165620 1,-1,1,0,-1,1,0,-1,-1,1,1,1,-2,-1,1,-1,2,2,-3,-1,1,0,-2,4,3,-4,-1,1,
%T A165620 0,-2,-4,7,4,-5,-1,1,1,2,-6,-7,11,5,-6,-1,1,-1,3,6,-13,-11,16,6,-7,-1,
%U A165620 1,0,-3,9,13,-24,-16,22,7,-8,-1,1
%N A165620 Riordan array ((1-x)/(1-x^4),x/(1+x^2)).
%C A165620 Diagonal sums are (-1)^n. Row sums have g.f. 1/(1+x^3).
%C A165620 The transform of the aerated Catalan numbers by this matrix is (-1)^n.
%C A165620 The transform of the shifted central binomial coefficient C(n+1,floor((n+1)/2)) is 1^n.
%C A165620 Factorizes as (1/(1+x),x)*(1/(1+x^2),x/(1+x^2)). Inverse is A165621.
%H A165620 P. Barry, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL12/Barry4/barry64.html">Symmetric Third-Order Recurring Sequences, Chebyshev Polynomials, and Riordan Arrays</a>, JIS 12 (2009) 09.8.6.
%F A165620 Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)(-1)^((j-k)/2)(1+(-1)^(j-k))C((j+k)/2,k)/2}.
%e A165620 Triangle begins
%e A165620 1,
%e A165620 -1, 1,
%e A165620 0, -1, 1,
%e A165620 0, -1, -1, 1,
%e A165620 1, 1, -2, -1, 1,
%e A165620 -1, 2, 2, -3, -1, 1,
%e A165620 0, -2, 4, 3, -4, -1, 1,
%e A165620 0, -2, -4, 7, 4, -5, -1, 1,
%e A165620 1, 2, -6, -7, 11, 5, -6, -1, 1,
%e A165620 -1, 3, 6, -13, -11, 16, 6, -7, -1, 1
%t A165620 (* The function RiordanArray is defined in A256893. *)
%t A165620 RiordanArray[(1 - #)/(1 - #^4)&, #/(1 + #^2)&, 11] // Flatten (* _Jean-François Alcover_, Jul 16 2019 *)
%K A165620 easy,sign,tabl
%O A165620 0,13
%A A165620 _Paul Barry_, Sep 22 2009