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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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