Numbers associated to Symmetric Differential Operators and the Bernoulli Numbers

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Abstract

By considering a certain symmetric differential operator we introduce a sequence of numbers {Ck}∞k=0, and clarify their properties, which are similar to those of the Bernoulli numbers. It is shown that the generating function of {Ck} is the hyperbolic tangent function, and some (maybe known) properties of the Bernoulli numbers are derived through those of Ck.

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