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}

Details 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} 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}

2007-12-23

arxiv.org/abs/0712.3946v1

Mathematics

Combinatorics

4 pages

Scientific paper

The 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.

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