\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{Kaneko1}
\citation{Kaneko2}
\citation{Kim-Kim}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction and background}{1}{section.1}}
\citation{Kaneko1}
\citation{Kaneko1}
\citation{Arakawa-Kaneko}
\citation{Arakawa-Kaneko}
\citation{Kaneko1}
\citation{Kaneko1}
\newlabel{1}{{1}{2}{\cite {Kaneko1}}{theorem.1}{}}
\newlabel{2}{{2}{2}{Closed formula \cite {Arakawa-Kaneko}}{theorem.2}{}}
\newlabel{3}{{3}{2}{Duality \cite {Arakawa-Kaneko}, \cite {Kaneko1}}{theorem.3}{}}
\newlabel{4}{{4}{2}{Symmetric formula \cite {Kaneko1}}{theorem.4}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Multi-poly-Bernoulli numbers}{2}{section.2}}
\citation{Kaneko1}
\newlabel{5}{{5}{3}{}{theorem.5}{}}
\newlabel{6}{{6}{3}{}{theorem.6}{}}
\newlabel{7}{{7}{3}{}{theorem.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Closed formula and duality}{4}{section.3}}
\newlabel{8}{{8}{4}{Closed formula}{theorem.8}{}}
\newlabel{9}{{9}{4}{}{theorem.9}{}}
\newlabel{10}{{10}{5}{Duality}{theorem.10}{}}
\bibcite{Arakawa-Kaneko}{1}
\bibcite{Carlitz}{2}
\bibcite{Graham, Knuth, Patashnik}{3}
\bibcite{Ireland-Rosen}{4}
\bibcite{Kaneko1}{5}
\bibcite{Kaneko2}{6}
\bibcite{Kim-Kim}{7}
\bibcite{Sanchez}{8}
\newlabel{11}{{11}{6}{Symmetric formula}{theorem.11}{}}
\newlabel{12}{{12}{6}{}{theorem.12}{}}