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A132092
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Numerators of Blandin-Diaz compositional Bernoulli numbers (B^sin)_3,n.
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18
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-1, -1, -11, -17, -563, -381, 55277, 242747, 406146379, 104180627, -398489682593, -169622229019, -6523856615663, -251077358513783, 35076901882951197, 2869253069531102351, 20717378005021857058651, 1335883610404565359777223, 27846976637614329871324177
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OFFSET
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1,3
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COMMENTS
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Denominators are A132093. 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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FORMULA
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(((x^3)/3!)/(sin(x)-x) = Sum_{n>=0} (B^sin)_3,n ((x^n)/n!).
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MAPLE
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A132092 := proc(n) local g; g := taylor(sin(x)-x, x=0, n+7) ; g := taylor(g/x^3, x=0, n+4) ; g := taylor( 1/6/g, x=0, n+4) ; n!*coeftayl(g, x=0, n) ; numer(%) ; end: for n from 0 to 40 by 2 do printf("%d, ", A132092(n)) ; od: # R. J. Mathar, May 25 2008
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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]]& // Numerator (* Jean-François Alcover, Mar 23 2020 *)
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PROG
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(PARI) my(N=40, x='x+O('x^N), v=apply(numerator, Vec(serlaplace(x^3/(6*(sin(x)-x)))))); vector(#v\2, k, v[2*k-1]) \\ Michel Marcus, Jan 24 2024
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CROSSREFS
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KEYWORD
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frac,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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