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The aim of this paper is to give an elementary proof of certain identities onbinomials and state an answer to Remark 8.2 in Takahiro Hayata, HarutakaKoseki, and Takayuki Oda, Matrix coefficients of the middle discrete series ofSU(2,2), J. Funct. Anal. 185 (2001), 297-341.

A binomial-coefficient identity arising from the middle discrete series of SU(2,2)