Walking into an absolute sum

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We investigate a combinatorial sum that can be interpreted as the moments of a random variate, measuring the absolute distance to the origin in a symmetric Bernoulli random walk. These sums can be characterized by polynomials related to the Dumont-Foata polynomials. The sums corresponding to the odd moments have a connection to the Gandhi polynomials and Genocchi numbers.
Related sequence in "The On-Line Encyclopedia of Integer Sequences" is A083061. See http://www.research.att.com/~njas/sequences/A083061

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Number Theory, Statistics Theory, 11B65; 60G50

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http://salesiana.dossiersoluciones.com/handle/123456789/131082

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606080
 http://arxiv.org/abs/math/0606080
 The Fibonacci Quarterly, 40(2):175-180, May 2002

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arXiv