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Polycosecant numbers and polycotangent numbers are introduced as level twoanalogues of poly-Bernoulli numbers. It is shown that polycosecant numbers andpolycotangent numbers satisfy many formulas similar to those of poly-Bernoullinumbers. However, there is much unknown about polycotangent numbers. Forexample, the zeta function interpolating them at non-positive integers has notyet been constructed. In this paper, we show some algebraic properties ofpolycosecant numbers and polycotangent numbers. Also, we generalize dualityformulas for polycosecant numbers which essentially include those forpolycotangent numbers.

On some properties of polycosecant numbers and polycotangent numbers