Eulerian polynomials of the second kind with \genfrac?

Question

The Eulerian polynomials of the second kind are defined as (see for example here)

E_n(x) = \sum_{m\ge0} \left\langle\!\!\left\langle n\atop  m\right\rangle\!\!\right\rangle  x^m .

I would like to use \genfrac to display this formula (similar as \genfrac is used to display the Eulerian numbers). Is this possible?

Answer 1

The following example takes the double brackets from package MnSymbol and uses \genfrac. An alternative would be a simple matrix environment.

\documentclass{article}
\usepackage{amsmath}

\makeatletter
\@ifpackageloaded{MnSymbol}{}{%
  \DeclareFontFamily{OMX}{MnSymbolE}{}
  \DeclareSymbolFont{largesymbolsMn}{OMX}{MnSymbolE}{m}{n}
  \SetSymbolFont{largesymbolsMn}{bold}{OMX}{MnSymbolE}{b}{n}
  \DeclareFontShape{OMX}{MnSymbolE}{m}{n}{
      <-6>  MnSymbolE5
     <6-7>  MnSymbolE6
     <7-8>  MnSymbolE7
     <8-9>  MnSymbolE8
     <9-10> MnSymbolE9
    <10-12> MnSymbolE10
    <12->   MnSymbolE12}{}
  \DeclareFontShape{OMX}{MnSymbolE}{b}{n}{
      <-6>  MnSymbolE-Bold5
     <6-7>  MnSymbolE-Bold6
     <7-8>  MnSymbolE-Bold7
     <8-9>  MnSymbolE-Bold8
     <9-10> MnSymbolE-Bold9
    <10-12> MnSymbolE-Bold10
    <12->   MnSymbolE-Bold12}{}
  \DeclareMathDelimiter{\llangle}{\mathopen}{largesymbolsMn}{'164}
                                            {largesymbolsMn}{'164}
  \DeclareMathDelimiter{\rrangle}{\mathclose}{largesymbolsMn}{'171}
                                            {largesymbolsMn}{'171}
}
\makeatother

\newcommand*{\Eulerian}[2]{%
  \mathinner{%
    \genfrac\llangle\rrangle{0pt}{}{#1}{#2}%
  }%
}

\begin{document}
\[
  E_n(x) = \sum_{m\ge0} \Eulerian{n}{m} x^m
\]
\end{document}

Answer 2

This solution uses \genfrac although not exclusively; however it does avoid \atop and works with MathJax.

\[
\sum_{m\ge0}\left\langle\!\!\!\genfrac<>{0pt}{}{n}{m}\!\!\!\right\rangle x^{m} 
\]