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%I #11 Feb 17 2019 09:15:16
%S 4,768,61440,165150720,47563407360,669692775628800,417888291992371200,
%T 2808209322188734464000,3055331742541343096832000,
%U 33437550590372458851729408000,56175084991825730870905405440000,7276695809501137874093602599075840000,17464069942802730897824646237782016000000
%N Denominators of the rational factor of Kaplan's series for the Dottie number.
%C 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.
%H Amiram Eldar, <a href="/A306254/b306254.txt">Table of n, a(n) for n = 0..100</a>
%H Ozaner Hansha, <a href="https://ozanerhansha.github.io/dottie-number">The Dottie Number</a>.
%H Ozaner Hansha, <a href="https://ozanerhansha.github.io/dottie-number/#kaplans-series">Kaplan's series</a>.
%H Samuel R. Kaplan, <a href="https://doi.org/10.1080/0025570X.2007.11953455">The Dottie Number</a>, Mathematics Magazine, Vol. 80, No. 1 (2007), pp. 73-74, <a href="https://www.maa.org/sites/default/files/Kaplan2007-131105.pdf">alternative link</a>.
%e The Kaplan series begins with d = Pi/4 - Pi^3/768 - Pi^5/61440 - 43*Pi^7/165150720 - ...
%t 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
%Y Cf. A003957, A177413, A182503, A200309, A212112, A212113, A302977.
%K nonn,frac
%O 0,1
%A _Amiram Eldar_, Feb 01 2019
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