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

1, 6, 180, 2835, 37800, 467775, 3831077250, 127702575, 2605132530000, 350813659321125, 15313294652906250, 147926426347074375, 2423034863565078262500, 144228265688397515625, 3952575621190533915703125, 84913182070036240111050234375, 999843529136357459316262500000

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 A368730 A135395

Adjacent sequences: A046986 A046987 A046988 * A046990 A046991 A046992

Keyword

nonn,easy,frac,nice

Author

N. J. A. Sloane

Status

approved