Euler numbers
Integers occurring in the coefficients of the Taylor series of 1/cosh t / From Wikipedia, the free encyclopedia
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In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion
- ,
Not to be confused with Eulerian number or Euler's number.
For other uses, see List of things named after Leonhard Euler § Numbers.
where is the hyperbolic cosine function. The Euler numbers are related to a special value of the Euler polynomials, namely:
The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition. They also occur in combinatorics, specifically when counting the number of alternating permutations of a set with an even number of elements.