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$$(x_1+\ldots+x_p)^n = \sum_{c_1+\ldots+c_p=n} \frac{n!}{c_1!\cdots c_p!}x_1^{c_1}\cdots x_p^{c_p}$$

As you can see, there's a space right above this line.

I think the correct thing to do would be to remove all the superfluous newlines before the opening and after the closing \$$.

Things are even worse if I want to separate ##\LaTeX## formulas from the rest of the text in the source code:

$$(x_1+\ldots+x_p)^n = \sum_{c_1+\ldots+c_p=n} \frac{n!}{c_1!\cdots c_p!}x_1^{c_1}\cdots x_p^{c_p}$$

Now I also have a space before the rendered formula.