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    Catalan numbers revisited

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    Wolstenholme and Morley, Primes and Pseudoprimes

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    In this note, we prove p2p^2 is a Morley pseudoprime (of order 2) iff p2p^2 is a Wolstenholme pseudoprime (of order 2) iff pp is a Wolstenholme prime iff pp is a Morley prime. Concerning pseudoprimes of order 1 that are not powers of primes, only 3 are known of Wolstenholme's type and absolutely none have yet been identified of Morley's type

    Simple closed form Hankel transforms based on the central coefficients of certain Pascal-like triangles

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    We study the Hankel transforms of sequences related to the central coefficients of a family of Pascal-like triangles. The mechanism of Riordan arrays is used to elucidate the structure of these transforms

    Why Delannoy numbers?

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    This article is not a research paper, but a little note on the history of combinatorics: We present here a tentative short biography of Henri Delannoy, and a survey of his most notable works. This answers to the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were the first general way to solve Ballot-like problems. These numbers appear in probabilistic game theory, alignments of DNA sequences, tiling problems, temporal representation models, analysis of algorithms and combinatorial structures.Comment: Presented to the conference "Lattice Paths Combinatorics and Discrete Distributions" (Athens, June 5-7, 2002) and to appear in the Journal of Statistical Planning and Inference
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