OFFSET
1,4
COMMENTS
A value of -1 is substituted at the poles where k=n.
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.
If the first column of zeros is removed from the triangle, each row is left-right symmetric with respect to the center value.
LINKS
G. C. Greubel, Rows n=1..100 of triangle, flattened
EXAMPLE
The triangle starts
0, -1;
0, -3, -1, -3;
0, -5, -8, -1, -8, -5;
0, -7, -3, -15, -1, -15, -3, -7;
0, -9, -16, -21, -24, -1, -24, -21, -16, -9;
0, -11, -5, -1, -2, -35, -1, -35, -2, -1, -5, -11;
0, -13, -24, -33, -40, -45, -48, -1, -48, -45, -40, -33, -24, -13;
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
tabf,sign,easy,frac
AUTHOR
Paul Curtz, Mar 13 2010
STATUS
approved