[Tex/LaTex] Expand a macro with parameters in tabular head

expansiontables

My eventual goal is to create my own tabular-like environment in which all entries are in math-mode by default, let's call it fancytable. (One requirement is that the first column be separated from the others by a line, but that shouldn't be the main problem.)

In Math mode in tabular without having to use $…$ everywhere I found how to approach the problem:

\documentclass{article}
\usepackage{array}
\usepackage{tabularx}
\begin{document}
\begin{tabular}{ >{$}c<{$} | >{$}c<{$} >{$}c<{$} }
    x & x^2 & x^3\\
    y & y^2 & y^4
\end{tabular}
\end{document}

but this is not what I'm looking for. (Note I am including tabularx because I need it for other purposes, I think it is relevant to mention.) The tabular may become large (say 15 columns) so writing >{$}c<{$} every time would be tedious. Also, some day I might change my mind and choose another lay-out, and changing all tables isn't really a thing I'm looking forward to. That's why I try to make it an environment.
Recently I asked how to copy and print a string a few times, in A command which concatenates a string an arbitrary number of times. So currently I have a command \repeatstring available and I expect to need it as in \repeatstring{5}{>{$}c<{$}}. (I have included its current definition below)
The first thing I tried is something like

\documentclass{article}
\usepackage{array}
\usepackage{tabularx}
% definition of \repeatstring left out, see below
\newenvironment{fancytable}[1]%
    {\begin{tabular}{ >{$}c<{$} | \repeatstring{#1}{>{$}c<{$}} } }
    {\end{tabular}}
\begin{document}
\begin{fancytable}{2} % the argument of fancytable is 1 less than the desired number of columns
    x & x^2 & x^3\\
    y & y^2 & y^4
\end{fancytable}
\end{document}

but tabular does not accept arbitrary commands in its header. I read trough How do I expand a macro into a tabular head? and tried to adapt the answers given there. Meanwhile I figured out that I should somehow expand \repeatstring before tabular sees what's going on in its head. I think defining a new columntype every time a fancytable is created is not a good thing to do (I fail to do it anyway, getting the same error as with the above approach). Some tries:

\documentclass{article}
\usepackage{array}
\usepackage{tabularx}
% definition of \repeatstring left out, see below
\newcommand\buildtabularhead{}
\newenvironment{fancytable}[1]%
    {%
    \renewcommand\buildtabularhead{ >{$}c<{$} | \repeatstring{#1}{>{$}c<{$}} }%
    \expandafter\tabular\expandafter{\buildtabularhead}}
    {\endtabular}
\begin{document}
\begin{fancytable}{2}
    x & x^2 & x^3\\
    y & y^2 & y^4
\end{fancytable}
\end{document}

(based on Matthew Leingang's answer) but I keep getting

Package array Error: Illegal pream-token (\repeatstring): `c' used.

as usual. The same with Bruno Le Floch's answer:

\documentclass{article}
\usepackage{array}
\usepackage{tabularx}
% definition of \repeatstring left out, see below
\makeatletter
    \newcolumntype{\expand}{}
    \long\@namedef{NC@rewrite@\string\expand}{\expandafter\NC@find}
\makeatother
\newcommand\mypream{}
\newenvironment{fancytable}[1]%
    {%
    \renewcommand\mypream{ >{$}c<{$} | \repeatstring{#1}{>{$}c<{$}} }%
    \begin{tabular}{\expand\mypream}}
    {\endtabular}
\begin{document}
\begin{fancytable}{2}
    x & x^2 & x^3\\
    y & y^2 & y^4
\end{fancytable}
\end{document}

I really don't know what to do. I read When to use \edef, \noexpand, and \expandafter? but didn't achieve to use \expandafter of \edef in the right way. I always and up with

Package array Error: Illegal pream-token (\repeatstring or \edef or \expandafter or \setcounter): `c' used.

\setcounter comes from my current definition of \repeatstring when I expand it:

\usepackage{etoolbox}
\newcounter{countdown}
\newcommand\concathere{}
\newcommand\repeatstring[2]{
    \setcounter{countdown}{#1}
    \renewcommand\concathere{}
    \whileboolexpr{test {\ifnumcomp{\thecountdown}{>}{0}}}{
        \addtocounter{countdown}{-1}
        \appto\concathere{#2}
        }
    \concathere
    }

Best Answer

The best solution to a simply 'repeat n-times' in a tabular preamble is indeed to use the * syntax as in barto's answer. However, if you do want to use a macro containing the preamble for some reason, using Bruno's solution to How do I expand a macro into a tabular head?, then the important thing to do is to make sure it contains exactly the preamble text. That requires a definition of \repeatstring which is expandable and the use of an \edef-like expansion of the code

\documentclass{article}
\usepackage{array}
\usepackage{tabularx}
\usepackage{xparse}

\ExplSyntaxOn
\DeclareExpandableDocumentCommand{\repeatstring}{mm}
 {
  \prg_replicate:nn { #1 } { #2 }
 }
\ExplSyntaxOff
\makeatletter
    \newcolumntype{\expand}{}
    \long\@namedef{NC@rewrite@\string\expand}{\expandafter\NC@find}
\makeatother
\newcommand\mypream{}
\makeatletter
\newenvironment{fancytable}[1]%
    {%
    \protected@edef\mypream{ >{$}c<{$} | \repeatstring{#1}{>{$}c<{$}} }%
    \begin{tabular}{\expand\mypream}}
    {\end{tabular}}
\makeatother
\begin{document}
\begin{fancytable}{2}
    x & x^2 & x^3\\
    y & y^2 & y^4
\end{fancytable}
\end{document}

In the above, I've used an expl3 based expandable repeat function to define \repeatstring (much the same as egeg's solution to A command which concatenates a string an arbitrary number of times), which means that when \protected@edef is applied \mypream ends up with definition >{$}c<{$} | >{$}c<{$}>{$}c<{$}, i.e. exactly what is needed in the tabular preamble.

All of this is needed as array avoids any expansion of the tabular preamble. Thus if you do

\renewcommand\mypream{ >{$}c<{$} | \repeatstring{#1}{>{$}c<{$}} }%

what array sees is exactly that: not a string of repeated >{$}c<{$} entries but the token \repeatstring, which is does not know (and so raises an error).

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