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A046988 Numerators of zeta(2*n)/Pi^(2*n). 18


%S -1,1,1,1,1,1,691,2,3617,43867,174611,155366,236364091,1315862,

%T 6785560294,6892673020804,7709321041217,151628697551,

%U 26315271553053477373,308420411983322,261082718496449122051,3040195287836141605382,5060594468963822588186

%N Numerators of zeta(2*n)/Pi^(2*n).

%C Equivalently, numerator of (-1)^(n+1)*2^(2*n-1)*Bernoulli(2*n)/(2*n)!. - _Lekraj Beedassy_, Jun 26 2003

%C An old name erroneously included "Numerators of Taylor series expansion of log(x/sin(x))"; that is now submitted as a distinct sequence A283301. - _Vladimir Reshetnikov_, Mar 04 2017

%D L. V. Ahlfors, Complex Analysis, McGraw-Hill, 1979, p. 205

%D T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 222, series for log(H(x)/x).

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.

%D CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.

%D 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.

%H J.P. Martin-Flatin, <a href="/A046988/b046988.txt">Table of n, a(n) for n = 0..250</a>

%H I. Song, <a href="http://dx.doi.org/10.1016/0377-0427(88)90274-9">A recursive formula for even order harmonic series</a>, J. Computational and Appl. Math., 21 (1988), 251-256.

%H Wolfram Research, <a href="http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/03/02/ShowAll.html">Some values of zeta(n)</a>

%H Wolfram Research, <a href="http://functions.wolfram.com/">A Formula for Zeta(2n)</a>

%e Numerator(zeta(0)/Pi^0) = -1. - _Artur Jasinski_, Mar 11 2010

%p seq(numer(Zeta(2*n)/Pi^(2*n)),n=1..24); # _Martin Renner_, Sep 07 2016

%t Table[Numerator[Zeta[2 n]/Pi^(2 n)], {n, 0, 30}] (* _Artur Jasinski_, Mar 11 2010 *)

%Y Cf. A002432 (denominators), A283301, A266214.

%K sign,easy,frac,nice

%O 0,7

%A _N. J. A. Sloane_

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Last modified October 19 22:55 EDT 2019. Contains 328244 sequences. (Running on oeis4.)