[Tex/LaTex] How to typeset an open circle with a dot inside, on an Internet forum

Question

I need to somehow put this symbol:

http://wstaw.org/m/2014/12/20/cauchy_cropped_cropped.png

And of course I mean this semi-open circle with a dot inside, right after "a_n".

I have seen it in a TeX document, this one: http://www.mimuw.edu.pl/~mmoszyns/Analiza-dla-informatykow-2014-15/analinf127.pdf (for example on page 48/49), where it is used to denote the Cauchy product.

I could not find neither this symbol nor a dotless open circle in The Comphehensive LaTeX symbol list (http:// www.tex.ac.uk/ctan/info/symbols/comprehensive/symbols-a4.pdf).

To make things even more awkward, I need to put it on an Internet forum. Due to that this idea \odot \!\! \white{\bullet} will not work: the background is not white, and even worse, it changes from post to post.

Thanks in advance for any idea how to do this.

EDIT: I do not want a normal, "closed" circle such as \odot or \bigodot, but an "open" one, as in the image above.
To be more specific: I want this: http://wstaw.org/m/2014/12/22/ccccc.png and not this: http://wstaw.org/m/2014/12/22/6718f3851aba6f5727da3da31bc74ee2.png

Also, since this is for an Internet forum, I can't \def anything.

Answer 1

EDITED to use \clipbox instead of white \rule overlay.

\documentclass{article}
\usepackage{amssymb,xcolor,trimclip}
\def\opendot{\mathbin{\clipbox{0pt 0pt .55ex 0pt}{$\odot$}}}
\begin{document}
$\sum_{n=0}^{+\infty} a_n \opendot \sum_{n=0}^{+\infty} b_n :=
  \sum_{n=0}^{+\infty} c_n$
\end{document}

ADDENDUM:

Apparently, the web-based input available to the OP did not allow for the clipped solution. However, I suggested (in the comments) something akin to {{\textsf{C}\kern-.85ex\raisebox{.9pt}{$\cdot$}\kern .25ex} which sufficed for the needs of the OP.

\documentclass{article}
\begin{document}
$x\mathbin{\textsf{C}\kern-.85ex\raisebox{.9pt}{$\cdot$}\kern .25ex}y$
\end{document}