Common
Euler number
Integers occurring in the coefficients of the Taylor series of 1/cosh t
Euler number
In mathematics, the Euler numbers are a sequence En of integers (sequence A122045 in the OEIS) defined by the Taylor series expansion 1cosht=2et+e−t=∑n=0∞Entnn!, where cosh(t) is the hyperbolic cosine function. The Euler numbers are related to a special value of the Euler polynomials, written here as en(t) so that they are not confused with the Euler numbers, En=2nen(12). 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.
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