Sun's curious identity

In combinatorics, Sun's curious identity is the following identity involving binomial coefficients, first established by Zhi-Wei Sun in 2002:

Proofs

After Sun's publication of this identity, five other proofs were obtained by various mathematicians:

  • Panholzer and Prodinger's proof via generating functions;
  • Merlini and Sprugnoli's proof using Riordan arrays;
  • Ekhad and Mohammed's proof by the WZ method;
  • Chu and Claudio's proof with the help of Jensen's formula;
  • Callan's combinatorial proof involving dominos and colorings.
gollark: when the chronoapioform interacts with a time-reversed version of itself
gollark: Wondrous!
gollark: Okay, recompiling.
gollark: I suppose IRC has its own formatting, so sure.
gollark: Interesting idea.

References

  • Callan, D. (2004), "A combinatorial proof of Sun's 'curious' identity" (PDF), INTEGERS: The Electronic Journal of Combinatorial Number Theory, 4: A05, arXiv:math.CO/0401216.
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