THIÉRY, Alain

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THIÉRY, Alain
Institut de Mathématiques de Bordeaux [IMB]

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Document de travail - Pré-publication

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In this note, the following \href{http://oeis.org/A157751}{conjecture of Clark Kimberling}(?) is proved \begin{conjecture} Let $(F_n(X))_{n\in \N}$ be the sequence of polynomials defined by $F_n(X) = (X+1)F_{n-1}(X)+F_{n-1}(-X)$ with initial term $F_0(X) = 1$. If $n$ is even then $F_n(X)$ has no real roots, and if $n$ is odd then $F_n(X)$ has exactly one real root, denoted by $r$, and if $n\ges 5$ then $0 < -r < n$. \end{conjecture}< Leer menos

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Note on the sequence A157751

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