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Search: id:A153359
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| A153359 |
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Scaled coefficients of the M. O. Rubinstein polynomials. |
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1
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| 1, -1, 1, -2, -1, 3, -2, -1, 2, 1, -152, -78, 125, 90, 15, -216, -114, 157, 135, 35, 3, -41424, -22444, 27552, 26551, 8505, 1197, 63, -66000, -36620, 40976, 42917, 15652, 2814, 252, 9
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The polynomials alpha_{k}(s) are defined in formula (1.4) in the paper cited below. The coefficients are in ascending order.
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REFERENCES
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M. O. Rubinstein, Identities for the Riemann Zeta function, arXiv:0812.2592v1 [math.NT] 14 Dec 2008.
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LINKS
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Identities for the Riemann Zeta function.
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FORMULA
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The coefficients of the polynomials alpha_{k}(s)*A053657(k) where alpha_{0}(s) = 1 and alpha_{k+1}(s) = (s-1)/(k+2)-sum(j=1..k,((j-(s-1)*(k-j+1))/(k-j+2))*alpha_{j}(s))/(k+1).
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EXAMPLE
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alpha_{0}(t) = 1 / 1;
alpha_{1}(t) = (-1 + t) / 2;
alpha_{2}(t) = (-2 - t + 3t^2) / 24;
alpha_{3}(t) = (-2 - t + 2t^2 + t^3) / 48;
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CROSSREFS
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A053657
Sequence in context: A026176 A026141 A089209 this_sequence A023510 A005678 A114905
Adjacent sequences: A153356 A153357 A153358 this_sequence A153360 A153361 A153362
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Peter Luschny (peter(AT)luschny.de), Dec 24 2008
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