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Search: id:A142155
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| A142155 |
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Coefficient series expansion of the polynomial of A073011: p(x)=(x^(10) + x^9 - x^8 - x^6 - x^5 - x^4 - x^3 + x + 1); by toral inverse. |
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+0
2
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| 1, -1, 2, -3, 6, -9, 17, -27, 48, -80, 139, -233, 402, -680, 1165, -1979, 3382, -5754, 9822, -16727, 28531, -48613, 82893, -141268, 240847, -410505, 699808, -1192838, 2033410, -3466085, 5908459, -10071512, 17168221, -29265017, 49885842, -85035890, 144953845, -247090156, 421194210
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Limit[a[n+1]/a[n],n->50]->-1.7046154656519101
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REFERENCES
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Weisstein, Eric W. "Polylogarithm." http://mathworld.wolfram.com/Polylogarithm.html "A number of remarkable identities exist for polylogarithms, including the amazing identity satisfied by Li_(17)(alpha_1^(-17)), where alpha_1=(x^(10)+x^9-x^8-x^6-x^5-x^4-x^3+x+1)_2 approx 1.17628 (Sloane's A073011) is the smallest Salem constant, i.e., the largest positive root of the polynomial in Lehmer's Mahler measure problem (Cohen et al. 1992; Bailey and Broadhurst 1999; Borwein and Bailey 2003, pp. 8-9). "
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FORMULA
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p(x)=(x^(10) + x^9 - x^8 - x^6 - x^5 - x^4 - x^3 + x + 1); q(x)=x^10*p(1/x):toral inverse; a(n) =coefficients of series(1/q(x)).
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MATHEMATICA
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p[x_] = (x^(10) + x^9 - x^8 - x^6 - x^5 - x^4 - x^3 + x + 1); q[x_] = Expand[x^10*p[1/x]]; a = Table[SeriesCoefficient[Series[1/q[x], {x, 0, 50}], n], {n, 0, 50}]
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CROSSREFS
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Cf A073011.
Sequence in context: A056532 A079289 A048811 this_sequence A092351 A048812 A048813
Adjacent sequences: A142152 A142153 A142154 this_sequence A142156 A142157 A142158
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KEYWORD
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sign,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 15 2008
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