Treffer: Bernoulli numbers with level 2

The content of this article covers the following topics: generating function, the Bernoulli numbers, the Euler numbers, the Bernoulli numbers of level 2, the Glaisher's R numbers, the Glaisher's H numbers, Complementary Euler numbers etc. The author examines the two-level number types of these numbers. He gives the relations between Stirling numbers of level 2, poly-Bernoulli numbers of level 2 and poly-Bernoulli numbers with the aid of the generating functions. By examining special cases, the author gives the relations between Bernoulli numbers of level 2 and classical Bernoulli numbers. In addition, he also finds new and interesting identities, relations and expressions among the Glaisher R numbers, complementary Euler numbers, the Stirling numbers, and Bernoulli numbers of level 2. These results given by the author have high application potential in mathematics, in combinatorial analysis, and in applied sciences.