generating function for the reciprocal alternating central binomial coefficients

It is also not very well known this relationMathworldPlanetmath:


where one clearly appreciate that the function on LHS generates the sequenceMathworldPlanetmath (-1)n(2nn)-1.

To obtain the relation above one should use some kind of software because for the function is “terrible” to calculate derivatives of any order. It is a little challenge to give a recursive formulaMathworldPlanetmathPlanetmath that gives the inversesPlanetmathPlanetmathPlanetmath of these alternating central binomial numbers, when evaluated at x=0 at those derivatives.

Title generating function for the reciprocal alternating central binomial coefficientsMathworldPlanetmath
Canonical name GeneratingFunctionForTheReciprocalAlternatingCentralBinomialCoefficients
Date of creation 2013-03-22 18:58:12
Last modified on 2013-03-22 18:58:12
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 14
Author juanman (12619)
Entry type Example
Classification msc 32A05
Classification msc 11B65
Classification msc 05A19
Classification msc 05A15
Classification msc 05A10