Here's an alternative. It provides left-alignment of the super/subscripts.
EDIT: In an effort to answer the OP's question, "Is there a way to get it so that the limits are left aligned with the horizontal midpoint of the close paren in automatic fashion?" The answer is yes. Here it is:
\documentclass[12pt]{article}
\usepackage[usestackEOL]{stackengine}
\parskip 1.5ex
\stackMath
\begin{document}
\newcommand\specparen[2]{%
\def\Krn{\kern1ex}%
\def\useanchorwidth{T}%
\setbox0=\hbox{\Krn\stackengine{0pt}{\scriptstyle#1}{\scriptstyle#2}{O}{c}{F}{F}{S}}%
\stackon[2pt]{\stackunder[2pt]{)}{\makebox[\wd0][l]{\Krn$\scriptstyle#1$}}}%
{\makebox[\wd0][l]{\Krn$\scriptstyle#2$}}%
}
$(x_j\specparen{j=1}{\infty} = y$
$(x_j\specparen{j=1}{j=\infty} = y$
\end{document}
Here is with \Krn
set to 0ex (which truly sets the sub/superscript midpoint to the center of the right paren):

and here it is with \Krn
set to 1ex (which does a controllable rightward shift of the sub/superscript):

$({\displaystyle\mathop{x_j}^\infty_{j=1}})$
? – Werner Mar 12 '14 at 5:33mathtools
command\mathclap{}
like this:)\limits_{\mathclap{j=1}}^{\mathclap{\infty}}
. This should get rid of the unwanted horizontal left space. – TheVal Mar 12 '14 at 6:08\mkern
, as Harish Kumar used. – TheVal Mar 12 '14 at 6:21