A combinatorial interpretation for the 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}

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dc.creatorCallan, David
dc.date2007-12-23
dc.date.accessioned2026-07-07T08:51:12Z
dc.date.available2026-07-07T08:51:12Z
dc.descriptionThe title identity appeared as Problem 75-4, proposed by P. Barrucand, 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.
dc.description4 pages
dc.identifierhttps://arxiv.org/abs/0712.3946
dc.identifierhttp://arxiv.org/abs/0712.3946
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144856
dc.subjectCombinatorics
dc.subject05A15
dc.titleA combinatorial interpretation for the 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}
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