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A046989 Denominators of Taylor series expansion in powers of x^2 of log(x/sin x). 2

%I

%S 1,6,180,2835,37800,467775,3831077250,127702575,2605132530000,

%T 350813659321125,15313294652906250,147926426347074375,

%U 2423034863565078262500,144228265688397515625,3952575621190533915703125,84913182070036240111050234375,999843529136357459316262500000

%N Denominators of Taylor series expansion in powers of x^2 of log(x/sin x).

%C For the numerators see A283301.

%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.

%F log(x/sin(x)) = Sum_{n>0} (2^(2*n-1)*(-1)^(n+1)*B(2*n)/(n*(2*n)!) * x^(2*n)). - _Ralf Stephan_, Apr 01 2015 [corrected by _Roland J. Etienne_, Apr 19 2016]

%e log(x/sin(x)) = 1/6*x^2 + 1/180*x^4 + 1/2835*x^6 + 1/37800*x^8 + 1/467775*x^10 + 691/3831077250*x^12 + ...

%t Join[{1},Denominator[Take[CoefficientList[Series[Log[x/Sin[x]],{x,0,50}], x],{3,-1,2}]]] (* _Harvey P. Dale_, Apr 27 2012 *)

%o (Sage) def a(n): return -numerator((n*factorial(2*n))/(2^(2*n-1)*(-1)^n*bernoulli(2*n))) /* _Ralf Stephan_, Apr 01 2015 */

%Y Cf. A283301 (numerators). A027641/A027642 (Bernoulli).

%K nonn,easy,frac,nice

%O 0,2

%A _N. J. A. Sloane_

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Last modified September 17 22:53 EDT 2019. Contains 327147 sequences. (Running on oeis4.)