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- W3209682937 abstract "In this note, the following href{http://oeis.org/A157751}{conjecture of Clark Kimberling}(?) is proved begin{conjecture} Let $(F_n(X))_{nin N}$ 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 $nges 5$ then $0 < -r < n$. end{conjecture}" @default.
- W3209682937 created "2021-11-08" @default.
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- W3209682937 date "2011-06-28" @default.
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- W3209682937 title "Note on the sequence A157751" @default.
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