Journal of Integer Sequences, Vol. 16 (2013), Article 13.7.6 |

Center for Research and Development in Mathematics and Applications

Department of Mathematics

University of Aveiro

Portugal

António Guedes de Oliveira

CMUP and Department of Mathematics

Faculty of Sciences

University of Porto

Portugal

**Abstract:**

We prove that, for every integer *a*, real numbers *k* and ,
and nonnegative integers *n*, *i* and *j*,

by presenting explicit expressions for its value. We use the identity to generalize a recent result of Chang and Xu, and end the paper by presenting, in explicit form, the ordinary generating function of the sequence , where .

by presenting explicit expressions for its value. We use the identity to generalize a recent result of Chang and Xu, and end the paper by presenting, in explicit form, the ordinary generating function of the sequence , where .

(Concerned with sequences A000302 A000984 A006256 A078995.)

Received February 8 2013;
revised versions received March 8 2013; July 26 2013; August 21 2013.
Published in *Journal of Integer Sequences*, August 22 2013.

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