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 A173264 #10 Jan 23 2019 08:29:37
%S A173264 1,1,-1,1,2,-1,1,-2,1,-1,1,2,0,2,-1,1,-2,-1,-4,3,-1,1,2,2,8,-7,4,-1,1,
%T A173264 -2,-3,-14,13,-11,5,-1,1,2,4,22,-20,24,-16,6,-1,1,-2,-5,-32,27,-46,40,
%U A173264 -22,7,-1,1,2,6,44,-33,82,-86,62,-29,8,-1,1,-2,-7,-58,37,-139,166,-148,91,-37,9,-1
%N A173264 T(0,k) = 1 and T(n,k) = [x^k] ((x - 2)*x^n + 1)/((x - 1)*(x + 1)^n) for n >= 1, square array read by descending antidiagonals (n >= 0, k >= 0).
%e A173264 Square array begins:
%e A173264 n\k | 0 1 2 3 4 5 6 7 8 ...
%e A173264 --------------------------------------------------
%e A173264 0 | 1 1 1 1 1 1 1 1 1 ...
%e A173264 1 | -1 2 -2 2 -2 2 -2 2 -2 ...
%e A173264 2 | -1 1 0 -1 2 -3 4 -5 6 ...
%e A173264 3 | -1 2 -4 8 -14 22 -32 44 -58 ...
%e A173264 4 | -1 3 -7 13 -20 27 -33 37 -38 ...
%e A173264 5 | -1 4 -11 24 -46 82 -139 226 -354 ...
%e A173264 6 | -1 5 -16 40 -86 166 -294 485 -754 ...
%e A173264 7 | -1 6 -22 62 -148 314 -610 1108 -1910 ...
%e A173264 8 | -1 7 -29 91 -239 553 -1163 2269 -4164 ...
%e A173264 ...
%t A173264 p[x_, n_] = If[n == 0, 1/(1 - x), (x^n - Sum[x^i, {i, 0, n - 1}])/( 1 + x)^n];
%t A173264 a = Table[Table[SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 0, 20}];
%t A173264 Flatten[Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]
%o A173264 (Maxima) (kk : 50, nn : 15)$
%o A173264 gf(n) := taylor(if n = 0 then 1/(1 - x) else ((x - 2)*x^n + 1)/((x - 1)*(x + 1)^n), x, 0, kk)$
%o A173264 T(n, k) := ratcoef(gf(n), x, k)$
%o A173264 create_list(T(k, n - k), n, 0, nn, k, 0, n);
%o A173264 /* _Franck Maminirina Ramaharo_, Jan 23 2019 */
%Y A173264 Cf. A173265, A173266.
%K A173264 sign,easy,tabl
%O A173264 0,5
%A A173264 _Roger L. Bagula_, Feb 14 2010
%E A173264 Edited by _Franck Maminirina Ramaharo_, Jan 23 2019