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(Note that e, the base of the natural logarithm, is also occasionally called Euler's number, as is the Euler characteristic.)
The oddindexed Euler numbers are all zero. The evenindexed ones have alternating signs. Some values are:
Some authors reindex the sequence in order to omit the oddnumbered Euler numbers with value zero, and/or change all signs to positive. This encyclopedia adheres to the convention adopted above.
The Euler numbers appear in the Taylor series expansion of the secant trigonometric function, and they also occur in combinatorics.
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