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%I #21 Jan 24 2024 17:36:30
%S 1,10,350,1050,57750,250250,2388750,2231250,1088106250,137156250,
%T 105761906250,2289218750,8842968750,51289218750,45049030468750,
%U 3563716406250,1099667378906250,4714260332031250,14142780996093750
%N Denominators of Blandin-Diaz compositional Bernoulli numbers (B^sin)_3,n.
%C Numerators and denominators given only for even n (odd n have numerators = 0).
%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. See Table 3.3.
%H Hector Blandin and Rafael Diaz, <a href="https://arxiv.org/abs/0708.0809">Compositional Bernoulli numbers</a>, p. 8, arXiv:0708.0809 [math.CO], 2007-2008.
%F (((x^3)/3!)/(sin(x)-x) = Sum_{n>=0} (B^sin)_3,n ((x^n)/n!).
%e -1, 0, -1/10, 0, -11/350, 0, -17,1050, 0, -563/57750, 0, -381/250250, 0.
%t m = 20;
%t ((x^3)/3!)/(Sin[x]-x) + O[x]^(2m) // CoefficientList[#, x]& // #*Range[0, 2m-2]!& // #[[;; ;; 2]]& // Denominator (* _Jean-François Alcover_, Mar 23 2020 *)
%o (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
%Y Numerators are A132092.
%Y Cf. A132094-A132099.
%K frac,nonn
%O 1,2
%A _Jonathan Vos Post_, Aug 09 2007
%E More terms from _R. J. Mathar_, May 25 2008
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