generating function for the reciprocal Catalan numbers

The series


whose coefficients are the reciprocal of the Catalan numbersDlmfMathworldPlanetmath (2nn)n+1, has as a generating function


To deduce such a formula the easy way, one starts from the generating function of the reciprocal central binomial coefficientsMathworldPlanetmath and having into account the relation


for each term in the corresponding series and applied to the functionMathworldPlanetmath in the region of uniform convergenceMathworldPlanetmath. Another method is almost exaclty the same like in the derivation of the generating function for the reciprocal central binomial coefficients.

Title generating function for the reciprocal Catalan numbers
Canonical name GeneratingFunctionForTheReciprocalCatalanNumbers
Date of creation 2013-03-22 19:05:12
Last modified on 2013-03-22 19:05:12
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 10
Author juanman (12619)
Entry type Derivation
Classification msc 05A19
Classification msc 05A15
Classification msc 05A10
Related topic CatalanNumbers