\BOOKMARK [1][-]{section.1}{Introduction}{}% 1
\BOOKMARK [1][-]{section.2}{Background}{}% 2
\BOOKMARK [1][-]{section.3}{Connection to compositions}{}% 3
\BOOKMARK [2][-]{subsection.3.1}{Definitions}{section.3}% 4
\BOOKMARK [2][-]{subsection.3.2}{Fuchs' result}{section.3}% 5
\BOOKMARK [2][-]{subsection.3.3}{Invariant sequences}{section.3}% 6
\BOOKMARK [3][-]{subsubsection.3.3.1}{Catalan numbers}{subsection.3.3}% 7
\BOOKMARK [3][-]{subsubsection.3.3.2}{Hermite polynomials}{subsection.3.3}% 8
\BOOKMARK [1][-]{section.4}{A nonlinear generalization}{}% 9
\BOOKMARK [2][-]{subsection.4.1}{Back to the Bernoulli numbers}{section.4}% 10
\BOOKMARK [2][-]{subsection.4.2}{Back to Bernoulli polynomials}{section.4}% 11
\BOOKMARK [2][-]{subsection.4.3}{Back to higher-order Bernoulli polynomials}{section.4}% 12
\BOOKMARK [2][-]{subsection.4.4}{Compositions with restricted summands}{section.4}% 13
\BOOKMARK [2][-]{subsection.4.5}{Sum of digits}{section.4}% 14
\BOOKMARK [1][-]{section.5}{A general formula for composition of functions}{}% 15
\BOOKMARK [1][-]{section.6}{Conclusion}{}% 16
\BOOKMARK [1][-]{section.7}{Acknowledgements}{}% 17