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Dec 21, 2016 at 17:40 comment added T. Amdeberhan As I mentioned in my answer, we can't expect to remove the hypergeometric sum because there in no "closed form" answer.
Dec 21, 2016 at 16:05 comment added LuHell Yes. The point is to get rid of the hypergeometrics for any x's. It seems hopeless.
Dec 20, 2016 at 16:38 comment added T. Amdeberhan The case $x=1$, has been dealt with at mathoverflow.net/questions/257349/equality-with-binomials
Dec 20, 2016 at 16:27 history answered Igor Rivin CC BY-SA 3.0