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A167407
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T(m,n) is -m if n=0, 1 elsewhere.
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1
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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
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OFFSET
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0,4
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COMMENTS
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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+-...
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LINKS
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Table of n, a(n) for n=0..96.
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EXAMPLE
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Triangle begins:
0;
-1,1;
-2,1,1;
-3,1,1,1;
-4,1,1,1,1;
...
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MATHEMATICA
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Flatten[Table[{-n, Table[1, {n}]}, {n, 0, 15}]] (* Harvey P. Dale, Apr 17 2015 *)
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CROSSREFS
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Cf. A061347, A166711, A166871.
Sequence in context: A080209 A347171 A127949 * A051340 A216764 A165430
Adjacent sequences: A167404 A167405 A167406 * A167408 A167409 A167410
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KEYWORD
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sign,tabl
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AUTHOR
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Jaume Oliver Lafont, Nov 03 2009, Nov 04 2009
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EXTENSIONS
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Revised by Jaume Oliver Lafont, Nov 11 2009
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STATUS
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approved
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