centered text/equations inside align environment

Question

is there a way to insert a centered line of text or mathematics inside an align-environment?

For example, in the code below, I'd like to have the \vdots between the equations above and below horizontally centered, completely ignoring the alignment markers:

\documentclass{article}
\begin{document}
\begin{align}
  f(1) &= 1 \\
  f(2) &= 2 \\
  \vdots & \\
  f(n) &= n f(n-1)
\end{align}
\end{document}

Answer 1

Like this?

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\noindent X\hrulefill X
  \begin{align}
  f(1) &= 1 \\
  f(2) &= 2 \\
  \shortintertext{\hfil    \vdots \hfil}
  f(n) &= n f(n-1) xxxxxxx
\end{align}
\end{document}

Answer 2

The “official” way of doing this is

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align}
  f(1) &= 1 \\
  f(2) &= 2 \\
       &\vdotswithin{=} \nonumber \\
  f(n) &= n f(n-1) xxxxxxx
\end{align}
\end{document}

But this doesn't answer the question, though. So… why would you like \vdots that ignore the content of align in a “text” line?