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A283301 Numerators of coefficients at even powers in Taylor series expansion of log(x/sin(x)). 2
0, 1, 1, 1, 1, 1, 691, 2, 3617, 43867, 174611, 155366, 236364091, 1315862, 3392780147, 6892673020804, 7709321041217, 151628697551, 26315271553053477373, 308420411983322, 261082718496449122051, 3040195287836141605382, 2530297234481911294093 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

This sequence shares many terms with A046988 (and appears to have been erroneously confused with it), but actually differs from it at indexes 0, 14, 22, 26, 28, 30, 38, 42, 44, 46, 50, 52, 54, 56, 58, 60, ...

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..22.

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

a[0] = 0; a[n_] := Numerator[((-1)^(n + 1) 2^(2 n - 1) BernoulliB[2 n])/(n (2 n)!)]; Table[a[n], {n, 0, 20}] (* or *)

Numerator@Table[SeriesCoefficient[Log[x/Sin[x]], {x, 0, 2n}], {n, 0, 20}]

CROSSREFS

Cf. A046989 (denominators), A046988.

Sequence in context: A001067 A141590 A276594 * A046988 A189683 A029825

Adjacent sequences:  A283298 A283299 A283300 * A283302 A283303 A283304

KEYWORD

nonn,frac,nice

AUTHOR

Vladimir Reshetnikov, Mar 04 2017

STATUS

approved

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Last modified May 13 19:36 EDT 2021. Contains 343868 sequences. (Running on oeis4.)