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Search: id:A046988
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| A046988 |
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Numerators of Taylor series expansion of log(x/sin x). Numerator of zeta(2n)/Pi^(2n). |
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+0
4
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| 0, 1, 1, 1, 1, 1, 691, 2, 3617, 43867, 174611, 155366, 236364091, 1315862, 6785560294, 6892673020804, 7709321041217, 151628697551, 26315271553053477373, 308420411983322, 261082718496449122051, 3040195287836141605382, 5060594468963822588186
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Equivalently, numerator of (-1)^n*2^(2n - 1)*Bernoulli(2n)/(2n)!. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 26 2003
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REFERENCES
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T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 222, series for log(H(x)/x).
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 84.
I. Song, A recursive formula for even order harmonic series, J. Computational and Appl. Math., 21 (1988), 251-256.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Wolfram Research, Some values of zeta(n)
Wolfram Research, A Formula for Zeta(2n)
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EXAMPLE
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log(x/sin(x)) = 1/6*x^2+1/180*x^4+1/2835*x^6+1/37800*x^8+1/467775*x^10+...
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MAPLE
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Zeta(2*n) # then extract numerator of rational part
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CROSSREFS
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Cf. A046989, A002432.
Sequence in context: A120084 A046968 A001067 this_sequence A029825 A106281 A127341
Adjacent sequences: A046985 A046986 A046987 this_sequence A046989 A046990 A046991
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KEYWORD
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nonn,easy,frac,nice
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AUTHOR
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njas
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