Divisibility properties of the $q$-tangent numbers
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- by George E. Andrews and Ira Gessel PDF
- Proc. Amer. Math. Soc. 68 (1978), 380-384 Request permission
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
- George E. Andrews, The theory of partitions, Encyclopedia of Mathematics and its Applications, Vol. 2, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976. MR 0557013
- Louis Comtet, Advanced combinatorics, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974. The art of finite and infinite expansions. MR 0460128, DOI 10.1007/978-94-010-2196-8 I. Gessel, Exponential generating functions $\pmod p$ and their q-analogs (in prep.).
- Richard P. Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J. Combinatorial Theory Ser. A 20 (1976), no. 3, 336–356. MR 409206, DOI 10.1016/0097-3165(76)90028-5
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 68 (1978), 380-384
- MSC: Primary 05A15
- DOI: https://doi.org/10.1090/S0002-9939-1978-0462960-0
- MathSciNet review: 0462960