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%I #10 Apr 17 2016 09:26:37
%S -1,-1,0,-1,-3,3,-1,-8,0,8,-1,-15,-5,5,15,-1,-24,-3,0,3,24,-1,-35,-21,
%T -7,7,21,35,-1,-48,-2,-16,0,16,2,48,-1,-63,-45,-1,-9,9,1,45,63,-1,-80,
%U -15,-40,-5,0,5,40,15,80,-1,-99,-77,-55,-33,-11,11,33,55,77,99,-1,-120,-6,-8,-3,-24,0,24,3,8,6,120,-1,-143,-117,-91,-65,-39,-13,13,39,65,91,117,143,-1,-168,-35,-112,-21,-56,-7,0,7,56,21,112,35,168,-1,-195,-165,-5,-105,-3,-5,-15
%N Triangle T(n,m) read by rows: numerator of 1/(n-m)^2-1/m^2, or -1 if m=0.
%C This is triangle A165507 with an additional column T(n,0)= -1.
%C The triangle is obtained from the infinite array shown in the comment in A172370 by starting in its row n, column 0 and reading diagonally upwards up to row n=1, column n-1.
%e The triangle starts in row n=1 with columns 0<=m<n as
%e -1;
%e -1,0,
%e -1,-3,3,
%e -1,-8,0,8,
%e -1,-15,-5,5,15,
%e -1,-24,-3,0,3,24,
%e -1,-35,-21,-7,7,21,35,
%e -1,-48,-2,-16,0,16,2,48,
%e -1,-63,-45,-1,-9,9,1,45,63,
%p A173651 := proc(n,m) if m = 0 then -1 ; else 1/(n-m)^2-1/m^2 ; numer(%) ; end if; end proc:
%Y Cf. A165795.
%K sign,tabl,frac,easy
%O 1,5
%A _Paul Curtz_, Nov 24 2010