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Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind

Chen Xue-Yan, Wu Lan, Lim Dongkyu, Qi Feng

Demonstratio Mathematica

2022

Vol. 55, nr 1

822--830

In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind, and supply simple proofs of series expansions of (hyperbolic) cosecant and cotangent functions.