Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

Details Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

2007-07-30

arxiv.org/abs/0707.4328v1

Discrete Math. 308 (2008), 4069--4078

Mathematics

Combinatorics

11 pages, to appear in Discrete Mathematics. See also http://math.univ-lyon1.fr/~guo

Scientific paper

10.1016/j.disc.2007.07.106

Motivated by the resemblance of a multivariate series identity and a finite
analogue of Euler's pentagonal number theorem, we study multiple extensions of
the latter formula. In a different direction we derive a common extension of
this multivariate series identity and two formulas of Lucas. Finally we give a
combinatorial proof of Lucas' formulas.

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