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Derivative Polynomials, Euler Polynomials, and Associated Integer Sequences

1999
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Electronic Journal of Combinatorics
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Let $P_n$ and $Q_n$ be the polynomials obtained by repeated differentiation of the tangent and secant functions respectively. From the exponential generating functions of these polynomials we develop relations among their values, which are then applied to various numerical sequences which occur as values of the $P_n$ and $Q_n$. For example, $P_n(0)$ and $Q_n(0)$ are respectively the $n$th tangent and secant numbers, while $P_n(0)+Q_n(0)$ is the $n$th André number. The André numbers, along with

doi:10.37236/1453
fatcat:cmpffxokhjcptni2fhfrollpbi