\documentclass{article}

\usepackage{mathtools}

\makeatletter

\def\ltcfrac[#1;#2]{\cfr@c#1,#2,\end}

\def\cfr@c#1,#2\end{\ifx#1\ldots\ddots\else#1\fi

  \ifx#2\end\else+{\strut1\hfill\over\displaystyle\cfr@c#2\end}\fi}

\makeatother

\begin{document}

\begin{align*}

[1;2,3,4]&=\ltcfrac[1;2,3,4]\\

\pi&=\ltcfrac[3;7,15,1,292,1,1,1,2,1,3,1,\ldots] \\

e&=\ltcfrac[2;1,2,1,1,4,1,1,6,1,1,8,1,1,\ldots]

\end{align*}

\end{document}