Geodesic
A combinatorial interpretation for an identity of Barrucand
Journal of integer sequences, Tome 11 (2008) no. 3
The binomial coefficient identity, $ \sum_{k=0}^{n}\binom{n}{k}\sum_{j=0}^{k}\binom{k}{j}^{3}= \sum_{k=0}^{n}\binom{n}{k}^{2}\binom{2k}{k}$, appeared as Problem 75-4 in Siam Review in 1975. The published solution equated constant terms in a suitable polynomial identity. Here we give a combinatorial interpretation in terms of card deals.
Classification : 05A15
Keywords: combinatorial identity, card deals (Concerned with sequences and ) 
@article{JIS_2008__11_3_a3,
     author = {Callan,  David},
     title = {A combinatorial interpretation for an identity of {Barrucand}},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {3},
     zbl = {1148.05006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a3/}
}
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Callan,  David. A combinatorial interpretation for an identity of Barrucand. Journal of integer sequences, Tome 11 (2008) no. 3. http://geodesic.mathdoc.fr/item/JIS_2008__11_3_a3/