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A046988
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Numerators of Taylor series expansion of log(x/sin(x)). For n>0, numerators of zeta(2*n)/Pi^(2*n).
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Equivalently, numerator of (-1)^n*2^(2*n-1)*Bernoulli(2*n)/(2*n)!. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 26 2003
Numerator(Zeta(0)/Pi^0) = -1 [From Artur Jasinski (grafix(AT)csl.pl), Mar 11 2010]
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REFERENCES
| L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205
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
| J.P. Martin-Flatin, Table of n, a(n) for n = 0..250
Wolfram Research, Some values of zeta(n)
Wolfram Research, A Formula for Zeta(2n)
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EXAMPLE
| 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
| Zeta(2*n) # then extract numerator of rational part
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MATHEMATICA
| Table[Numerator[Zeta[2 n]/Pi^(2 n)], {n, 1, 30}] (*Artur Jasinski*) [From Artur Jasinski (grafix(AT)csl.pl), Mar 11 2010]
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CROSSREFS
| Cf. A046989, A002432.
Sequence in context: A046968 A001067 A141590 * A189683 A029825 A180320
Adjacent sequences: A046985 A046986 A046987 * A046989 A046990 A046991
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KEYWORD
| nonn,easy,frac,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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