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arXiv · 2104.09726

Stirling numbers with level $2$ and poly-Bernoulli numbers with level $2$

Takao Komatsu
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Abstract

In this paper, we introduce poly-Bernoulli numbers with level $2$, related to the Stirling numbers of the second kind with level $2$, and study several properties of poly-Bernoulli numbers with level $2$ from their expressions, relations, and congruences. Poly-Bernoulli numbers with level $2$ have strong connections with poly-Cauchy numbers with level $2$. In a special case, we can determine the denominators of Bernoulli numbers with level $2$ by showing a von Staudt-Clausen like theorem.

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Takao Komatsu. 2021-04-20. Stirling numbers with level $2$ and poly-Bernoulli numbers with level $2$. https://arxiv.org/abs/2104.09726

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