Journal of Integer Sequences, Vol. 23 (2020), Article 20.6.4

On Polycosecant Numbers


Masanobu Kaneko
Faculty of Mathematics
Kyushu University
Motooka 744, Nishi-ku
Fukuoka 819-0395
Japan

Maneka Pallewatta
Graduate School of Mathematics
Kyushu University
Motooka 744, Nishi-ku
Fukuoka 819-0395
Japan

Hirofumi Tsumura
Department of Mathematical Sciences
Tokyo Metropolitan University
1-1, Minami-Ohsawa
Hachioji, Tokyo 192-0397
Japan

Abstract:

We introduce and study a "level two" generalization of the poly-Bernoulli numbers, which may also be regarded as a generalization of the cosecant numbers. We prove a recurrence relation, two exact formulas, and a duality relation for negative upper-index numbers.

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(Concerned with sequences A001896 A001897 A008277 A027641 A027642 A099594

Received August 1 2019; revised versions received April 12 2020; May 12 2020; May 18 2020. Published in Journal of Integer Sequences, June 9 2020.

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