Thursday, May 23, 2019

combinatorics - Proving an identity involving binomial coefficients and fractions

I've been trying to prove the following formula (for n>1 natural, a,b non-zero reals), but I don't know where to start.




nj=1(n1j1)(aj+1bn+1)(ab)j1(bab)nj=ab



Wolfram says it's right, but so far I've been unable to give a proof. I wonder if there's a combinatorial proof to it. Any help, hint or reference will be much appreciated.

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