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Some properties of a sequence similar to generalized Euler numbers. (English) Zbl 1263.11036
Summary: We introduce the sequence $$\{U^{(x)}_n\}$$ given by generating function $$(1/(e^t + e^{-t} - 1))^x = \sum^\infty_{n=0}U^{(x)}_n(t^n/n!)(|t| < (1/3)\pi, 1^x := 1)$$ and establish some explicit formulas for the sequence $$\{U^{(x)}_n\}$$. Several identities involving the sequence $$\{U {(x)}_n\}$$, Stirling numbers, Euler polynomials, and the central factorial numbers are also presented.
##### MSC:
 11B68 Bernoulli and Euler numbers and polynomials 11B73 Bell and Stirling numbers 11B65 Binomial coefficients; factorials; $$q$$-identities
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##### References:
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