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Search: id:A052137
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| A052137 |
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Denominators of power series coefficients of a(x) satisfying a(a(a(x)))= arctan(x). |
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+0
2
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| 1, 9, 135, 25515, 45927, 12629925, 4433103675, 1396427657625, 23739270179625, 21920842083865725, 34525326282088516875, 8734907549368394769375, 17688187787470999407984375, 413903594226821386146834375
(list; graph; listen)
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OFFSET
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0,2
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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+i). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2007
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MAPLE
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interface(labelling=false) : a := 0 : mPow := 15 : 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, ", denom(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. A052136. See also A048602, A048603, etc.
Sequence in context: A082760 A112426 A034723 this_sequence A003376 A081876 A139760
Adjacent sequences: A052134 A052135 A052136 this_sequence A052138 A052139 A052140
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KEYWORD
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nonn,frac,easy,nice
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AUTHOR
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njas, 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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