A167407 T(m,n) is -m if n=0, 1 elsewhere.

0, -1, 1, -2, 1, 1, -3, 1, 1, 1, -4, 1, 1, 1, 1, -5, 1, 1, 1, 1, 1, -6, 1, 1, 1, 1, 1, 1, -7, 1, 1, 1, 1, 1, 1, 1, -8, 1, 1, 1, 1, 1, 1, 1, 1, -9, 1, 1, 1, 1, 1, 1, 1, 1, 1, -10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -13, 1, 1, 1, 1, 1

Offset: 0

Author

Jaume Oliver Lafont, Nov 03 2009, Nov 04 2009

Keywords

• sign
• tabl

Comments

This triangle encodes a family of conditionally convergent series for the logarithm of positive integers, according to: log(m)=Sum_{n>0} T(m-1,n mod m)/n.

The second row of the triangle, m=1, corresponds to Mercator's series:

log(2)=1-1/2+1/3-1/4+1/5-1/6+-...

Examples

			Triangle begins:
   0;
  -1,1;
  -2,1,1;
  -3,1,1,1;
  -4,1,1,1,1;
  ...
		

Crossrefs

Cf. A061347, A166711, A166871.

Programs

Mathematica

Flatten[Table[{-n,Table[1,{n}]},{n,0,15}]] (* Harvey P. Dale, Apr 17 2015 *)

Extensions

Revised by Jaume Oliver Lafont, Nov 11 2009