login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052135 Denominators of coefficients in function a(x) such that a(a(a(x))) = sin x. 3
1, 18, 1080, 408240, 29393280, 215550720, 648499737600, 953294614272000, 2333665215737856000, 7183021534041120768000, 232066849561328517120000, 723095875143672151080960000, 74189636789740762700906496000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also denominators of coefficients in function a(x) such that a(a(a(x))) = sinh x.

REFERENCES

W. C. Yang, Composition equations, preprint, 1999.

LINKS

Table of n, a(n) for n=0..12.

MATHEMATICA

n = 13; m = 2 n - 1 (* m = maximal degree *); a[x_] = Sum[c[k] x^k, {k, 1, m, 2}] ; coes = DeleteCases[ CoefficientList[Series[a @ a @ a @ x - Sin[x], {x, 0, m}], x] // Rest , 0]; Do[s[k] = Solve[coes[[1]] == 0] // First; coes = coes /. s[k] // Rest, {k, 1, n}]

(CoefficientList[a[x] /. Flatten @ Array[s, n], x] // Denominator // Partition[#, 2] &)[[All, 2]]

(* Jean-François Alcover, May 04 2011 *)

CROSSREFS

Cf. A052132, A052134. See also A048602, A048603, etc.

Sequence in context: A301651 A159379 A323571 * A033518 A333006 A064564

Adjacent sequences:  A052132 A052133 A052134 * A052136 A052137 A052138

KEYWORD

nonn,frac,easy,nice

AUTHOR

N. J. A. Sloane, Jan 22 2000

EXTENSIONS

More terms from Vladeta Jovovic, Jul 16 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 2 14:48 EST 2021. Contains 349445 sequences. (Running on oeis4.)