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.
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
KEYWORD
nonn,frac,nice
AUTHOR
Vladimir Reshetnikov, Mar 04 2017
STATUS
approved