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Search: id:A052136
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| A052136 |
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Numerators of power series coefficients of a(x) satisfying a(a(a(x)))= arctan(x). |
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2
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| 1, -1, 4, -263, 181, -19417, 2650183, -334415182, 2505796264, -1075533383968, 644250947168711, -35934792935656882, 59703596150692742866, -2784264154855168826899, 13245106337447512956269, 145404446885533849363819862, -576405412549008975387674250194
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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W. C. Yang, Composition equations, preprint, 1999.
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FORMULA
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a(x)=sum_{n=0,1,2,3...} A052136(n)/A052137(n)*x^(2n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2007
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MAPLE
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interface(labeling=false) : a := 0 : mPow := 17 : for i from 0 to mPow do a := a+alph[2*i+1]*x^(2*i+1) ; od: a2 := 0 : for i from 0 to mPow do a2 := a2+alph[2*i+1]*a^(2*i+1) ; od: a2 := taylor(a2, x=0, 2*mPow+2) : a2 := convert(a2, polynom) : a3 := 0 : for i from 0 to mPow do a3 := a3+alph[2*i+1]*a2^(2*i+1) ; od: for i from 0 to mPow do tanCoef[2*i+1] := coeftayl(arctan(x), x=0, 2*i+1) ; od: a3 := taylor(a3, x=0, 2*mPow+2) : a3 := convert(a3, polynom) : for i from 0 to mPow do tozer := coeftayl(a3, x=0, 2*i+1) : alph[2*i+1] := op(1, [solve(tozer=tanCoef[2*i+1], alph[2*i+1])]) : printf("%d, ", numer(alph[2*i+1])) ; ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2007
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CROSSREFS
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Cf. A052137. See also A048602, A048603, etc.
Sequence in context: A003382 A112982 A061788 this_sequence A089667 A119008 A108134
Adjacent sequences: A052133 A052134 A052135 this_sequence A052137 A052138 A052139
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KEYWORD
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sign,frac,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 22 2000
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2007
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