Some applications of the generalized Eulerian numbers

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Abstract

In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is related to an autonomous first-order differential equation, solutions of which are used to obtain integral representations of some numbers, including the Bernoulli numbers.

MSC

11B68
05A15

Keywords

Eulerian number
Second-order Eulerian number
Bernoulli number
Autonomous differential equation
Integral representation

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