A Combinatorial Proof for the Alternating Convolution of the Central Binomial Coefficients

Michael Z. Spivey
2014 The American mathematical monthly  
We give a combinatorial proof of the identity for the alternating convolution of the central binomial coefficients. Our proof entails applying an involution to certain colored permutations and showing that only permutations containing cycles of even length remain.
doi:10.4169/amer.math.monthly.121.06.537 fatcat:f3hzdhforjghrg7q4fq5gihmtm