A174233 - OEIS

%I #13 Jan 06 2019 03:58:08

%S 0,-1,0,-3,-1,-3,0,-5,-8,-1,-8,-5,0,-7,-3,-15,-1,-15,-3,-7,0,-9,-16,

%T -21,-24,-1,-24,-21,-16,-9,0,-11,-5,-1,-2,-35,-1,-35,-2,-1,-5,-11,0,

%U -13,-24,-33,-40,-45,-48,-1,-48,-45,-40,-33,-24,-13,0,-15,-7,-39,-3,-55,-15,-63

%N Triangle T(n,k) read by rows: the numerator of 1/n^2 - 1/(k-n)^2, 0 <= k < 2n.

%C A value of -1 is substituted at the poles where k=n.

%C 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 If the first column of zeros is removed from the triangle, each row is left-right symmetric with respect to the center value.

%H G. C. Greubel, <a href="/A174233/b174233.txt">Rows n=1..100 of triangle, flattened</a>

%e The triangle starts

%e   0,  -1;

%e   0,  -3,  -1,  -3;

%e   0,  -5,  -8,  -1,  -8,  -5;

%e   0,  -7,  -3, -15,  -1, -15,  -3,  -7;

%e   0,  -9, -16, -21, -24,  -1, -24, -21, -16,  -9;

%e   0, -11,  -5,  -1,  -2, -35,  -1, -35,  -2,  -1,  -5, -11;

%e   0, -13, -24, -33, -40, -45, -48,  -1, -48, -45, -40, -33, -24, -13;

%p 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 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 Cf. A175779, A172370, A061035, A174190, A120072.

%K tabf,sign,easy,frac

%O 1,4

%A _Paul Curtz_, Mar 13 2010