\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{schwenk}
\citation{bcg}
\citation{bouton}
\HyPL@Entry{0<</S/D>>}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{1}{section.1}}
\newlabel{intro}{{1}{1}{Introduction}{section.1}{}}
\@writefile{toc}{\contentsline {section}{\numberline {2}Results for the basic version}{4}{section.2}}
\newlabel{basic}{{2}{4}{Results for the basic version}{section.2}{}}
\newlabel{pn1}{{1}{4}{Results for the basic version}{equation.2.1}{}}
\newlabel{pnresult}{{2}{5}{Results for the basic version}{equation.2.2}{}}
\newlabel{binomial}{{1}{5}{}{theorem.1}{}}
\newlabel{case0}{{3}{6}{}{theorem.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {3}Observations on the sequences}{6}{section.3}}
\newlabel{seq}{{3}{6}{Observations on the sequences}{section.3}{}}
\@writefile{toc}{\contentsline {section}{\numberline {4}Results for general cases}{7}{section.4}}
\newlabel{general}{{4}{7}{Results for general cases}{section.4}{}}
\newlabel{rk}{{4}{7}{}{theorem.4}{}}
\newlabel{abpq}{{5}{9}{}{theorem.5}{}}
\newlabel{ab1/2}{{6}{9}{}{theorem.6}{}}
\newlabel{a1an}{{7}{10}{}{theorem.7}{}}
\@writefile{toc}{\contentsline {section}{\numberline {5}Further observations and open questions}{11}{section.5}}
\newlabel{furtherandopen}{{5}{11}{Further observations and open questions}{section.5}{}}
\newlabel{pnapprox}{{3}{12}{Further observations and open questions}{equation.5.3}{}}
\citation{bo}
\newlabel{integral}{{4}{13}{Further observations and open questions}{equation.5.4}{}}
\newlabel{In}{{5}{13}{Further observations and open questions}{equation.5.5}{}}
\bibcite{bo}{1}
\bibcite{bcg}{2}
\bibcite{bouton}{3}
\bibcite{schwenk}{4}
\@writefile{toc}{\contentsline {section}{\numberline {6}Acknowledgement}{14}{section.6}}