A173651 Triangle T(n,m) read by rows: numerator of 1/(n-m)^2-1/m^2, or -1 if m=0.

-1, -1, 0, -1, -3, 3, -1, -8, 0, 8, -1, -15, -5, 5, 15, -1, -24, -3, 0, 3, 24, -1, -35, -21, -7, 7, 21, 35, -1, -48, -2, -16, 0, 16, 2, 48, -1, -63, -45, -1, -9, 9, 1, 45, 63, -1, -80, -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

Offset: 1

Author

Paul Curtz, Nov 24 2010

Keywords

• sign
• tabl
• frac
• easy

Comments

This is triangle A165507 with an additional column T(n,0)= -1.

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.

Examples

			The triangle starts in row n=1 with columns 0<=m<n as
-1;
-1,0,
-1,-3,3,
-1,-8,0,8,
-1,-15,-5,5,15,
-1,-24,-3,0,3,24,
-1,-35,-21,-7,7,21,35,
-1,-48,-2,-16,0,16,2,48,
-1,-63,-45,-1,-9,9,1,45,63,
		

Crossrefs

Cf. A165795.

Programs

Maple

A173651 := proc(n,m) if m = 0 then -1 ; else 1/(n-m)^2-1/m^2 ; numer(%) ; end if; end proc: