OEIS A000281: Expansion of cos x / cos 2x

We explore the integer sequence obtained by multiplying the (2n)-th Taylor coefficient of cos x / cos 2x by (2n)!, revealing a dramatically growing but highly structured sequence. We trace its history (Gleicher, Sloan), its connections to Euler and Bernoulli polynomials and continued fractions, and its precise asymptotics (Simon Plouffe), showing how a simple trigonometric ratio hides a deep arithmetical world.

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