Card Deals, Lattice Paths, Abelian Words and Combinatorial Identities
نویسندگان
چکیده
We give combinatorial interpretations of several related identities associated with the names Barrucand, Strehl and Franel, including one for the Apéry numbers, ∑n k=0 (n k )(n+k k ) ∑k j=0 (k j 3 = ∑n k=0 (n k )2(n+k k 2 . The combinatorial constructs employed are derangement-type card deals as introduced in a previous paper on Barrucand’s identity, labeled lattice paths and, following a comment of Jeffrey Shallit, abelian words over a 3-letter alphabet.
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