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A046989 Denominators of Taylor series expansion in powers of x^2 of log(x/sin x). 2
1, 6, 180, 2835, 37800, 467775, 3831077250, 127702575, 2605132530000, 350813659321125, 15313294652906250, 147926426347074375, 2423034863565078262500, 144228265688397515625, 3952575621190533915703125, 84913182070036240111050234375, 999843529136357459316262500000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For the numerators see A283301.

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.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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]

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 + 691/3831077250*x^12 + ...

MATHEMATICA

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

PROG

(Sage) def a(n): return -numerator((n*factorial(2*n))/(2^(2*n-1)*(-1)^n*bernoulli(2*n))) /* Ralf Stephan, Apr 01 2015 */

CROSSREFS

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

Sequence in context: A024278 A062240 A253779 * A210358 A135395 A141121

Adjacent sequences:  A046986 A046987 A046988 * A046990 A046991 A046992

KEYWORD

nonn,easy,frac,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 14 17:12 EST 2018. Contains 317210 sequences. (Running on oeis4.)