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A167407 T(m,n) is -m if n=0, 1 elsewhere. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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+-...

Triangle begins:

0;

-1,1;

-2,1,1;

-3,1,1,1;

-4,1,1,1,1;

...

LINKS

Table of n, a(n) for n=0..96.

MATHEMATICA

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

CROSSREFS

Cf. A061347, A166711, A166871.

Sequence in context: A175465 A080209 A127949 * A051340 A216764 A165430

Adjacent sequences:  A167404 A167405 A167406 * A167408 A167409 A167410

KEYWORD

sign,tabl

AUTHOR

Jaume Oliver Lafont, Nov 03 2009, Nov 04 2009

EXTENSIONS

Revised by Jaume Oliver Lafont, Nov 11 2009

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)