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Divisibility properties of the $ q$-tangent numbers

Authors: George E. Andrews and Ira Gessel
Journal: Proc. Amer. Math. Soc. 68 (1978), 380-384
MSC: Primary 05A15
MathSciNet review: 0462960
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Abstract: The q-tangent number $ {T_{2n + 1}}(q)$ is shown to be divisible by $ (1 + q)(1 + {q^2}) \cdots (1 + {q^n})$. Related divisibility questions are discussed.

References [Enhancements On Off] (What's this?)

  • [1] George E. Andrews, The theory of partitions, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. Encyclopedia of Mathematics and its Applications, Vol. 2. MR 0557013
  • [2] Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128
  • [3] I. Gessel, Exponential generating functions $ \pmod p$ and their q-analogs (in prep.).
  • [4] Richard P. Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J. Combinatorial Theory Ser. A 20 (1976), no. 3, 336–356. MR 0409206

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Article copyright: © Copyright 1978 American Mathematical Society