Geodesic
Proof of Sun's conjecture on the divisibility of certain binomial sums
Victor J. W. Guo1
1East China Normal University
The electronic journal of combinatorics, Tome 20 (2013) no. 4
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In this paper, we prove the following result conjectured by Z.-W. Sun:$$(2n-1){3n\choose n}|\sum_{k=0}^{n}{6k\choose 3k}{3k\choose k}{6(n-k)\choose 3(n-k)}{3(n-k)\choose n-k}$$by showing that the left-hand side divides each summand on the right-hand side.
DOI : 10.37236/3100
Classification : 11B65, 05A10, 11A07
Mots-clés : congruences, binomial coefficients, super Catalan numbers, Stirling's formula

Victor J. W. Guo  1

1 East China Normal University 
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     author = {Victor J. W. Guo},
     title = {Proof of {Sun's} conjecture on the divisibility of certain binomial sums},
     journal = {The electronic journal of combinatorics},
     year = {2013},
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Victor J. W. Guo. Proof of Sun's conjecture on the divisibility of certain binomial sums. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3100

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