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A054525
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Triangle T(n,k): T(n,k) = mu(n/k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n).
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92
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1, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 1, -1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A051731 = the inverse of this triangle = A129372 * A115361. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 15 2007
If a column T(n,0)=0 is added, these are the coefficients of the necklace polynomials multiplied by n [Moree,Metropolis]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2008]
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LINKS
| Pieter Moree, The formal series Witt transform, Discr. Math. 295 (2005), 143-160. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2008]
N. Metropolis, G.-C. Rota, Witt vectors and the algebra of necklaces, Adv. Math. 50 (1983), 95-125. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 11 2008]
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FORMULA
| Matrix inverse of triangle A051731, where A051731(n, k) = 1 if k|n, 0 otherwise. - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 09 2006
Equals = A129360 * A115369 as infinite lower triangular matrices. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 15 2007
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EXAMPLE
| Triangle begins:
1;
-1,1;
-1,0,1;
0,-1,0,1;
-1,0,0,0,1;
1,-1,-1,0,0,1;
-1,0,0,0,0,0,1;
0,0,0,-1,0,0,0,1; ...
Matrix inverse is triangle A051731:
1;
1,1;
1,0,1;
1,1,0,1;
1,0,0,0,1;
1,1,1,0,0,1;
1,0,0,0,0,0,1;
1,1,0,1,0,0,0,1; ...
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CROSSREFS
| Cf. A054521.
Cf. A051731.
Cf. A129360, A115369.
Sequence in context: A115952 A115524 A117198 * A174852 A065333 A127972
Adjacent sequences: A054522 A054523 A054524 * A054526 A054527 A054528
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KEYWORD
| sign,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 09 2000
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