A306254 Denominators of the rational factor of Kaplan's series for the Dottie number.

4, 768, 61440, 165150720, 47563407360, 669692775628800, 417888291992371200, 2808209322188734464000, 3055331742541343096832000, 33437550590372458851729408000, 56175084991825730870905405440000, 7276695809501137874093602599075840000, 17464069942802730897824646237782016000000

Offset: 0

Author

Amiram Eldar, Feb 01 2019

Keywords

• nonn
• frac

Comments

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

Examples

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

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.

Crossrefs

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

Programs

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