How do I proof this combinatorial identity Unicorn Meta Zoo #1: Why another podcast? Announcing the arrival of Valued Associate #679: Cesar ManaraAlternative combinatorial proof for $sumlimits_r=0^nbinomnrbinomm+rn=sumlimits_r=0^nbinomnrbinommr2^r$Number of way to invite my friends over for dinner on 5 nightsHelp with how to prepare the inductive step of a strong induction exercise.Source and/or combinatorial interpretation for $F_n+k = sum_i=0^k binomkiF_n-i$Another combinatorial identity of McKayExpectation of the fraction a random function covers its rangeFind a conjecture for $F_1+F_2+…+F_n$Proof involving Fibonacci number and binomial coefficientCombinatorial proof of $n choose 1 + n choose 3 +cdots = n choose 0 + n choose 2+cdots$Generating function of even Fibonacci numbers
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