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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A306254 Denominators of the rational factor of Kaplan's series for the Dottie number. 1
4, 768, 61440, 165150720, 47563407360, 669692775628800, 417888291992371200, 2808209322188734464000, 3055331742541343096832000, 33437550590372458851729408000, 56175084991825730870905405440000, 7276695809501137874093602599075840000, 17464069942802730897824646237782016000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

These are the denominators of the unique sequence of rational numbers r_n such that d=Sum_{n>=0} (r_n*Pi^(2n+1)) (where d is the Dottie number A003957). The numerators are in A302977.

LINKS

Amiram Eldar, Table of n, a(n) for n = 0..100

Ozaner Hansha, The Dottie Number.

Ozaner Hansha, Kaplan's series.

Samuel R. Kaplan, The Dottie Number, Mathematics Magazine, Vol. 80, No. 1 (2007), pp. 73-74, alternative link.

EXAMPLE

The Kaplan series begins with d = Pi/4 - Pi^3/768 - Pi^5/61440 - 43*Pi^7/165150720 - ...

MATHEMATICA

f[x_] := x - Cos[x]; g[x_] := InverseFunction[f][x]; s = {}; Do[AppendTo[s, Denominator[(-1/2)^n * 1/n! * Derivative[n][g][Pi/2]]], {n, 1, 30, 2}]; s

CROSSREFS

Cf. A003957, A177413, A182503, A200309, A212112, A212113, A302977.

Sequence in context: A181200 A308141 A284813 * A068112 A007725 A102195

Adjacent sequences:  A306251 A306252 A306253 * A306255 A306256 A306257

KEYWORD

nonn,frac

AUTHOR

Amiram Eldar, Feb 01 2019

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 June 12 14:32 EDT 2021. Contains 344957 sequences. (Running on oeis4.)