Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas
arXiv:0707.4328 · doi:10.1016/j.disc.2007.07.106
Abstract
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.
arXiv comment11 pages, to appear in Discrete Mathematics. See also http://math.univ-lyon1.fr/~guo