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 A174233 #13 Jan 06 2019 03:58:08
%S A174233 0,-1,0,-3,-1,-3,0,-5,-8,-1,-8,-5,0,-7,-3,-15,-1,-15,-3,-7,0,-9,-16,
%T A174233 -21,-24,-1,-24,-21,-16,-9,0,-11,-5,-1,-2,-35,-1,-35,-2,-1,-5,-11,0,
%U A174233 -13,-24,-33,-40,-45,-48,-1,-48,-45,-40,-33,-24,-13,0,-15,-7,-39,-3,-55,-15,-63
%N A174233 Triangle T(n,k) read by rows: the numerator of 1/n^2 - 1/(k-n)^2, 0 <= k < 2n.
%C A174233 A value of -1 is substituted at the poles where k=n.
%C A174233 The triangle is created by selecting the first 2, 4, 6 etc elements of the array shown in A172370, equivalent to attaching the initial elements of the rows of A172157 to the rows of A174190.
%C A174233 If the first column of zeros is removed from the triangle, each row is left-right symmetric with respect to the center value.
%H A174233 G. C. Greubel, <a href="/A174233/b174233.txt">Rows n=1..100 of triangle, flattened</a>
%e A174233 The triangle starts
%e A174233 0, -1;
%e A174233 0, -3, -1, -3;
%e A174233 0, -5, -8, -1, -8, -5;
%e A174233 0, -7, -3, -15, -1, -15, -3, -7;
%e A174233 0, -9, -16, -21, -24, -1, -24, -21, -16, -9;
%e A174233 0, -11, -5, -1, -2, -35, -1, -35, -2, -1, -5, -11;
%e A174233 0, -13, -24, -33, -40, -45, -48, -1, -48, -45, -40, -33, -24, -13;
%p A174233 A173233 := proc(n,k) if k = n then -1 ; else 1/n^2-1/(k-n)^2 ; numer(%) ; end if; end proc: # _R. J. Mathar_, Jan 06 2011
%t A174233 T[n_, n_] := -1; T[n_, k_] := 1/n^2 - 1/(k - n)^2; Table[Numerator[T[n, k]], {n, 1, 20}, {k, 0, 2 n - 1}]//Flatten (* _G. C. Greubel_, Sep 19 2018 *)
%Y A174233 Cf. A175779, A172370, A061035, A174190, A120072.
%K A174233 tabf,sign,easy,frac
%O A174233 1,4
%A A174233 _Paul Curtz_, Mar 13 2010