All the predefined mathematical symbols from the TeX package are listed below. More symbols are available from extra packages. Sections remaining to be done: Table 3 onwards from symbols.pdf. Scott Pakin, The Comprehensive LaTeX Symbol List, 2017.
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It's incorrect to detach the ! meaning “factorial” from the symbol preceding it, because it's a modifier similar to a prime or a subscript and is not a punctuation symbol. In case you have a factorial followed by an ordinary symbol...
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Begin{document} This is the old notation for the factorial $\oldfactorial{n}$. Some other text in order to wrap the line and see what happens with interline spacing below the symbol.
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Begin{document} \[. X\fallingfactorial{n}={\overbrace{x(x-1)\dots(x-n+1)}^{\text{$n$ factors}}} \] \. End{document}. After adding. \usepackage[euler-digits]{eulervm}. You get. By the way, this is exactly how it's realized in gkpmac.tex (the macro file used for typesetting “Concrete Mathematics”...
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