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A335258 Denominators of expansion of arctanh(tan(x)) (odd powers only). 1
1, 3, 3, 315, 567, 155925, 93555, 638512875, 127702575, 1856156927625, 7795859096025, 49308808782358125, 56894779364259375, 1298054391195577640625, 95646113035463615625, 122529844256906551386796875, 47570410123269602303109375, 2405873491984360136479756640625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The denominators of a series used by Johann Heinrich Lambert (1728-1777) in expressing the relationship between a circular sector and a hyperbolic sector.

Lambert gave a(1)-a(4).

REFERENCES

Johann Heinrich Lambert: ``Mémoire sur quelques propriétés remarquables des quantités transcendentes circulaires et logarithmiques,'' Histoire de l'Académie Royale des Sciences et Belles-Lettres, 1761, volume XVII, Berlin, 1768, pp. 265-322.

LINKS

Table of n, a(n) for n=1..18.

Lambert's use of the series

EXAMPLE

arctan(tanh(x)) = x - 2/3*x^3 + 2/3*x^5 - 244/315*x^7 + 554/567*x^9 ...

arctanh(tan(x)) = x + 2/3*x^3 + 2/3*x^5 + 244/315*x^7 + 554/567*x^9 ...

MATHEMATICA

Denominator @ CoefficientList[ Series[ArcTanh[Tan[x]], {x, 0, 36}], x][[2 ;; -1 ;; 2]] (* Amiram Eldar, Jun 04 2020 *)

PROG

(PARI) my(x='x+O('x^40), v=Vec(atanh(tan(x)))); apply(denominator, vector(#v\2, k, v[2*k-1])) \\ Michel Marcus, Jun 05 2020

CROSSREFS

Cf. A335257.

Sequence in context: A113466 A007301 A009715 * A292163 A242886 A221947

Adjacent sequences:  A335255 A335256 A335257 * A335259 A335260 A335261

KEYWORD

nonn

AUTHOR

Denis Roegel, May 28 2020

STATUS

approved

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)