Journal of Integer Sequences, Vol. 15 (2012), Article 12.1.3

Sums of Products of Poly-Bernoulli Numbers of Negative Index

Ken Kamano
Department of Mathematics
Osaka Institute of Technology
5-16-1, Omiya, Asahi, Osaka 535-8585


We give a formula that expresses a sum of products of poly-Bernoulli numbers of negative index as a linear combination of poly-Bernoulli numbers. More generally, we show that if a two-variable formal power series satisfies a certain partial differential equation, then its coefficients satisfy this type of formula. As an appendix, we solve this partial differential equation.

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(Concerned with sequences A027649 A027650 A027651.)

Received September 7 2011; revised version received November 29 2011. Published in Journal of Integer Sequences, December 26 2011.

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