Further triangles of Seidel-Arnold type and continued fractions related to Euler and Springer numbers
\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.
scientific article; zbMATH DE number 820049