generating function for the reciprocal central binomial coefficients

It is well known that the sequenceMathworldPlanetmath called central binomial coefficientsMathworldPlanetmath is defined by (2nn) and whose initial terms are 1,2,6,20,70,252, has a generating function 11-4x. But it is less known the fact that the function


has ordinary power series


This means that such a function is a generating function for the reciprocals (2nn)-1.

From that expression we can see that the numerical series n=0(2nn)-1 sums 4(3+π6)33 which has the approximate value 1,7363998587187151.


1) Renzo Sprugnoli, Sum of reciprocals of the Central Binomial Coefficients, Integers: electronic journal of combinatorial number theory, 6 (2006) A27, 1-18

Title generating function for the reciprocal central binomial coefficients
Canonical name GeneratingFunctionForTheReciprocalCentralBinomialCoefficients
Date of creation 2013-03-22 18:58:09
Last modified on 2013-03-22 18:58:09
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 12
Author juanman (12619)
Entry type Result
Classification msc 05A19
Classification msc 11B65
Classification msc 05A10
Classification msc 05A15
Synonym convergent seriesMathworldPlanetmathPlanetmath