DoubleDecker

\documentclass{scrartcl}
\usepackage{mathtools}
\usepackage{amsmath}
\usepackage{scalerel}

\makeatletter
\newcommand*\doubledecker[2]
{\mathpalette{\doubledeckeraux{#1}{#2}}\relax}
\newcommand*\doubledeckeraux[3]
{\vcenter{\offinterlineskip
		\ialign{$\ifx\textstyle#3\scriptstyle
			\else\ifx\scriptstyle#3\scriptscriptstyle
			\fi\fi
			(\hfil##\hfil)\m@th$\cr
			#1\cr
			#2\cr}}}
\makeatother

\newcommand*\DDoubledecker[2]{
	\scaleleftright{\leftdoubleparens}{{\mathstrut #1 \atop \mathstrut #2}}{\rightdoubleparens}
}

\newcommand\leftdoubleparens{\vbox{\hbox{(}\vskip-2.85pt\hbox{(}}}
\newcommand\rightdoubleparens{\vbox{\hbox{)}\vskip-2.85pt\hbox{)}}}

\begin{document}
    The doubledecker numbers are: $\sum_{k=0}^n \binom{n}{k} \doubledecker{k}{n}$

    \medskip
    The doubledecker numbers are : $\sum_{k=0}^n \binom{n}{k} \DDoubledecker{k}{n}$

    \begin{flalign}
	D(n,k) &= \sum_{k=0}^n \binom{n}{k} \doubledecker{k}{n}  \\ % Manuel
	D(n,k) &= \sum_{k=0}^n \binom{n}{k} \DDoubledecker{k}{n}    % Hagen
    \end{flalign}

\end{document}