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A046988 Numerators of Taylor series expansion of log(x/sin(x)). For n>0, numerators of zeta(2*n)/Pi^(2*n). 7
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; text; internal format)
OFFSET

0,7

COMMENTS

Equivalently, numerator of (-1)^n*2^(2*n-1)*Bernoulli(2*n)/(2*n)!. - Lekraj Beedassy, Jun 26 2003

Numerator(Zeta(0)/Pi^0) = -1 [From Artur Jasinski, Mar 11 2010]

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.

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)

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+...

MAPLE

Zeta(2*n) # then extract numerator of rational part

MATHEMATICA

Table[Numerator[Zeta[2 n]/Pi^(2 n)], {n, 1, 30}] (*Artur Jasinski*) [From Artur Jasinski, Mar 11 2010]

CROSSREFS

Cf. A046989, A002432.

Sequence in context: A046968 A001067 A141590 * A189683 A029825 A180320

Adjacent sequences:  A046985 A046986 A046987 * A046989 A046990 A046991

KEYWORD

nonn,easy,frac,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified September 17 01:33 EDT 2014. Contains 246831 sequences.