Treffer: Further Triangles of Seidel-Arnold Type and Continued Fractions Related to Euler and Springer Numbers: Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers

Title:
Further Triangles of Seidel-Arnold Type and Continued Fractions Related to Euler and Springer Numbers: Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers
Authors:
D. Dumont
Source:
Advances in Applied Mathematics. 16:275-296
Publisher Information:
Elsevier BV, 1995.
Publication Year:
1995
Subject Terms:
Continued fractions and generalizations, Continued fractions, Applied Mathematics, Exact enumeration problems, generating functions, 0102 computer and information sciences, 01 natural sciences, continued fraction, Seidel type triangles, Other combinatorial number theory, generating functions, Springer numbers, Genocchi numbers, 0101 mathematics, Bernoulli and Euler numbers and polynomials, Euler numbers
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Language:
English
ISSN:
0196-8858
DOI:
10.1006/aama.1995.1014
Access URL:
https://zbmath.org/820049
https://doi.org/10.1006/aama.1995.1014
https://www.sciencedirect.com/science/article/pii/S0196885885710147
https://www.sciencedirect.com/science/article/abs/pii/S0196885885710147
https://core.ac.uk/display/82652244
Rights:
Elsevier Non-Commercial
Accession Number:
edsair.doi.dedup.....f96f6b22710af9cada5b4c21f09793d7
Database:
OpenAIRE

Weitere Informationen

\textit{V. I. Arnold} [Russ. Math. Surv. 47, No. 1, 1-51 (1992; Zbl 0791.05001)] introduced two pairs of triangles of numbers that lead to simple algorithms for computing Springer numbers (arising from the expansion \(S(x)= {\text{cosh } x\over \text{cosh } 2x}+ {\text{sinh } x\over \text{cosh } 2x}\)) [\textit{T. A. Springer}, Nieuw Arch. Wiskd. III. Ser. 19, 30-36 (1971; Zbl 0224.05002)]. The author proved this approach on the base of Seidel type triangles [the author and \textit{G. Viennot}, Ann. Discrete Math. 6, 77-87 (1980; Zbl 0449.10011)], using only exponential generating functions. The method is carried over to ordinary generating functions, and their continued fraction expansions are given-- -in particular, for Euler, Springer, and Genocchi numbers. In addition, a new pair of triangles for Euler numbers is introduced, and the ``median'' Euler numbers are defined.