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Further divisibility properties of the $ q$-tangent numbers


Author: Dominique Foata
Journal: Proc. Amer. Math. Soc. 81 (1981), 143-148
MSC: Primary 05A15
DOI: https://doi.org/10.1090/S0002-9939-1981-0589157-8
MathSciNet review: 589157
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Abstract: The $ q$-tangent number $ {T_{2n + 1}}(q)$ is shown to be divisible by $ {(1 + q)^{a(n,1)}}{(1 + {q^2})^{a(n,2)}} \cdots {(1 + {q^n})^{a(n,n)}}$, where the $ a(n,i)$'s are positive integers having the maximal property that $ a(n,1) + a(n,2) + \cdots + a(n,n) = 2n$ whenever $ n$ is a power of 2.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0589157-8
Article copyright: © Copyright 1981 American Mathematical Society

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