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%I #11 Sep 20 2018 00:35:15
%S -1,-1,-3,-1,-8,-5,-1,-15,-3,-7,-1,-24,-21,-16,-9,-1,-35,-2,-1,-5,-11,
%T -1,-48,-45,-40,-33,-24,-13,-1,-63,-15,-55,-3,-39,-7,-15,-1,-80,-77,
%U -8,-65,-56,-5,-32,-17,-1,-99,-6,-91,-21,-3,-4,-51,-9,-19,-1,-120,-117,-112
%N Triangle T(n,m) = numerator of 1/n^2 - 1/m^2, read by rows, with T(n,0) = -1.
%C The triangle obtained by negating the values of the triangle A120072 and adding a row T(n,0) = -1.
%H G. C. Greubel, <a href="/A172157/b172157.txt">Rows n=1..100 of triangle, flattened</a>
%e The full array of numerators starts in row n=1 with columns m>=0 as:
%e -1...0...3...8..15..24..35..48..63..80..99. A005563
%e -1..-3...0...5...3..21...2..45..15..77...6. A061037, A070262
%e -1..-8..-5...0...7..16...1..40..55...8..91. A061039
%e -1.-15..-3..-7...0...9...5..33...3..65..21. A061041
%e -1.-24.-21.-16..-9...0..11..24..39..56...3. A061043
%e -1.-35..-2..-1..-5.-11...0..13...7...5...4. A061045
%e -1.-48.-45.-40.-33.-24.-13...0..15..32..51. A061047
%e -1.-63.-15.-55..-3.-39..-7.-15...0..17...9. A061049
%e The triangle is the portion below the main diagonal, left from the zeros, 0<=m<n.
%t T[n_, 0] := -1; T[n_, k_] := 1/n^2 - 1/k^2; Table[Numerator[T[n, k]], {n, 1, 100}, {k, 0, n - 1}] // Flatten (* _G. C. Greubel_, Sep 19 2018 *)
%Y Cf. A172370, A174233, A165795.
%K sign,frac,easy,tabl
%O 1,3
%A _Paul Curtz_, Jan 27 2010
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