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A132093
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Denominators of Blandin-Diaz compositional Bernoulli numbers (B^sin)_3,n.
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3
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1, 10, 350, 1050, 57750, 250250, 2388750, 2231250, 1088106250, 137156250, 105761906250, 2289218750, 8842968750, 51289218750, 45049030468750, 3563716406250, 1099667378906250, 4714260332031250, 14142780996093750
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OFFSET
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1,2
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COMMENTS
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Numerators are A132092. Numerators and denominators given only for even n (odd n have numerators = 0).
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199. See Table 3.3.
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LINKS
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Table of n, a(n) for n=1..19.
Hector Blandin and Rafael Diaz, Compositional Bernoulli numbers, p. 8, arXiv:0708.0809 [math.CO], 2007-2008.
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FORMULA
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(((x^3)/3!)/(sin(x)-x) = SUM[n=0..infinity] (B^sin)_3,n ((x^n)/n!).
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EXAMPLE
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-1, 0, -1/10, 0, -11/350, 0, -17,1050, 0, -563/57750, 0, -381/250250, 0.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A132092-A132106.
Sequence in context: A171583 A060704 A220185 * A339411 A217507 A217508
Adjacent sequences: A132090 A132091 A132092 * A132094 A132095 A132096
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KEYWORD
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frac,nonn
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AUTHOR
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Jonathan Vos Post, Aug 09 2007
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EXTENSIONS
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More terms from R. J. Mathar, May 25 2008
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STATUS
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approved
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