Summary: 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.

05A15

combinatorial identity, card deals (Concerned with sequences and )