OFFSET
0,2
COMMENTS
Numerators and denominators given only for even n (odd n have numerators = 0).
REFERENCES
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. See Table 3.3.
LINKS
Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, p. 8, arXiv:0708.0809 [math.CO], 2007-2008.
FORMULA
((x^3)/3!)/(sin(x)-x) = Sum_{n>=0} (B^sin)_3,n ((x^n)/n!).
EXAMPLE
-1, 0, -1/10, 0, -11/350, 0, -17,1050, 0, -563/57750, 0, -381/250250, 0.
MATHEMATICA
m = 20;
((x^3)/3!)/(Sin[x]-x) + O[x]^(2m) // CoefficientList[#, x]& // #*Range[0, 2m-2]!& // #[[;; ;; 2]]& // Denominator (* Jean-François Alcover, Mar 23 2020 *)
PROG
(PARI) my(N=40, x='x+O('x^N), v=apply(denominator, Vec(serlaplace(x^3/(6*(sin(x)-x)))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Jan 24 2024
CROSSREFS
KEYWORD
frac,nonn
AUTHOR
Jonathan Vos Post, Aug 09 2007
EXTENSIONS
More terms from R. J. Mathar, May 25 2008
Offset corrected as suggested by Andrew Howroyd. - N. J. A. Sloane, Sep 22 2024
STATUS
approved