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Search: id:A121376
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| A121376 |
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Numerator of PolyLog[ -n, 1/n ]. |
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+0
4
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| -1, 6, 33, 380, 3535, 189714, 285929, 319735800, 1160703963, 145739620510, 86294277091, 10914811650686580, 60229285882649, 163637596919801624970, 3392462704290802545, 669084376596453009616, 370468452361579892135179, 157145213515550643044429571846
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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PolyLog[n,z] = Sum[ z^k/k^n, {k,1,Infinity} ]. PolyLog[ -n,1/n] = Sum[ k^n/n^k, {k,1,Infinity}] for n>1. n divides a(n). p^k divides a(p^k) for all prime p and integer k>0. p^k divides a(p^k-1) for prime p>2 and integer k>0.
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Polylogarithm.
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FORMULA
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a(n) = Numerator[ PolyLog[ -n, 1/n ] ]. For n>1 a(n) = Numerator[ (-1)^n * PolyLog[ -n, n ] ].
For n>1, a(n) is the numerator of n*A122778(n)/(n-1)^(n+1) = Sum[k=0..n] A(n,k)*n^(k+1)/(n-1)^(n+1). For n>1, a(n) = n * A122778(n)/gcd(A122778(n),(n-1)^(n+1)). - Max Alekseyev (maxale(AT)gmail.com), Sep 11 2006
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EXAMPLE
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PolyLog[ -n,1/n] begins -1/12, 6, 33/8, 380/81, 3535/512, 189714/15625, ...
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MATHEMATICA
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Numerator[Table[PolyLog[ -n, 1/n], {n, 1, 40}]]
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CROSSREFS
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Cf. A119758.
Sequence in context: A137970 A024079 A118094 this_sequence A046707 A112289 A011798
Adjacent sequences: A121373 A121374 A121375 this_sequence A121377 A121378 A121379
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KEYWORD
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frac,sign
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Sep 06 2006
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