  Recently, Feng, Kuznetsov and Yang discovered a very general reduction
formula for a sum of products of the generalized hypergeometric functions (J.
Math. Anal. Appl. 443(2016), 116--122). The main goal of this note is to
present a generalization of a particular case of their identity when the
generalized hypergeometric function is reduced to the Kummer function 1F1. Our
generalized formula contains an additional integer shift in the bottom
parameter of the Kummer function. The key ingredient of the proof is a
summation formula for the Clausen series 3F2(1) with two integral parameter
differences of opposite sign. In the ultimate section of the paper we prove
another formula for a particular product difference of the Kummer functions in
terms of a linear combination of these functions.
