A175779 - OEIS

%I #10 Sep 20 2018 00:35:48

%S 1,0,1,0,3,1,0,5,8,1,0,7,3,15,1,0,9,16,21,24,1,0,11,5,1,2,35,1,0,13,

%T 24,33,40,45,48,1,0,15,7,39,3,55,15,63,1,0,17,32,5,56,65,8,77,80

%N Triangle T(n,m) read by rows: numerator of 1/(n-m)^2 - 1/n^2.

%C T(n,0) is set to zero at the pole m=0. T(n,n) is otherwise set to 1 at the pole n=m.

%C This is the triangle A061035 augmented by a diagonal of 1's.

%C Essentially the same information is in A120072, A166492, A172157 and A174233.

%H G. C. Greubel, <a href="/A175779/b175779.txt">Rows n=0..100 of triangle, flattened</a>

%e The triangle starts in row n=0 with columns 0<=m<=n as:

%e .1.

%e .0..1.

%e .0..3..1.

%e .0..5..8..1.

%e .0..7..3.15..1.

%e .0..9.16.21.24..1.

%e .0.11..5..1..2.35..1.

%e .0.13.24.33.40.45.48..1.

%e .0.15..7.39..3.55.15.63..1.

%e .0.17.32..5.56.65..8.77.80..1.

%e .0.19..9.51..4..3.21.91..6.99..1.

%t T[n_, n_] := 1; T[n_, k_] := 1/(n - k)^2 - 1/n^2; Table[Numerator[T[n, k]], {n, 0, 20}, {k, 0, n}] // Flatten  (* _G. C. Greubel_, Sep 19 2018 *)

%Y Cf. A172157, A166925, A171522 (denominators)

%K nonn,frac,tabl

%O 0,5

%A _Paul Curtz_, Dec 04 2010