Cook, Charles K.; Bacon, Michael R.; Hillman, Rebecca A. Higher order boustrophedon transforms for certain well-known sequences. (English) Zbl 1401.11068 Fibonacci Q. 55, No. 3, 201-208 (2017). Summary: A review of the boustrophedon transform is presented and transforms of several familiar sequences are obtained. In addition higher transforms are also investigated. Representations of the transform will be given in terms of members of the original sequence using the Euler Up-Down number coefficients. MSC: 11B83 Special sequences and polynomials PDFBibTeX XMLCite \textit{C. K. Cook} et al., Fibonacci Q. 55, No. 3, 201--208 (2017; Zbl 1401.11068) Full Text: Link Online Encyclopedia of Integer Sequences: Euler or up/down numbers: e.g.f. sec(x) + tan(x). Also for n >= 2, half the number of alternating permutations on n letters (A001250). Boustrophedon transform of all-1’s sequence. Expansion of exp(x)*(1 + tan(x))/(1 - tan(x)). Number of alternating permutations of order n. Expansion of e.g.f. exp(x)*(tan(x)+sec(x))^2. Expansion of e.g.f. exp(x)*(1+tan(x))/((1-tan(x))*(tan(x)+sec(x))). Expansion of e.g.f. (tan x + sec x)^3. Expansion of e.g.f. exp(x)*(tan x + sec x)^3. Expansion of e.g.f. (tan x + sec x)*(E.g.f. for A000738). Expansion of e.g.f. (tan x + sec x)^2*(E.g.f. for A000738).