|
Search: id:A052136
|
|
|
| A052136 |
|
Numerators of power series coefficients of a(x) satisfying a(a(a(x)))= arctan(x). |
|
+0
2
|
|
| 1, -1, 4, -263, 181, -19417, 2650183, -334415182, 2505796264, -1075533383968, 644250947168711, -35934792935656882, 59703596150692742866, -2784264154855168826899, 13245106337447512956269, 145404446885533849363819862, -576405412549008975387674250194
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
W. C. Yang, Composition equations, preprint, 1999.
|
|
FORMULA
|
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
|
|
MAPLE
|
interface(labelling=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
|
|
CROSSREFS
|
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
|
|
KEYWORD
|
sign,frac,easy,nice
|
|
AUTHOR
|
njas, Jan 22 2000
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2007
|
|
|
Search completed in 0.002 seconds
|
