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欧拉数En是一个整数数列,由下列泰勒级数展开式定义:

奇数项的欧拉数皆为零,偶数项的欧拉数正负相间,开首为:

E0 = 1
E2 = -1
E4 = 5
E6 = -61
E8 = 1,385
E10 = -50,521
E12 = 2,702,765
E14 = -199,360,981
E16 = 19,391,512,145
E18 = -2,404,879,675,441 (OEIS数列A028296

部分作者会把数列中的奇数项移除,只替偶数项编序,并且把负号转为正号。这里依从上段所用的惯例。

欧拉数在正割sec x双曲正割sech x泰勒级数出现。双曲正割就是定义中使用的函数。组合数学也会用到欧拉数。此外,在关于自然数负幂的交错和中也涉及到欧拉数。

欧拉多项式是以欧拉数构造。

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