I encountered this notation while reading the following paper: On the efficient calculation of a linear combination of chi-square random variables with an application in counting string vacua.
In it, one can read
Unfortunately I cannot figure out the meaning of the set "2 ℕₒ + 1". I suppose it could mean that r must be odd, but I am not sure. Also, does the summation of $X_i$ and $Y_i$ indicate that the number of chi-squared variables must always be even?
$2\mathbb N_0+1$ means $\{2n+1\mid n\in\mathbb N_0\}$
$=\{2\times0+1,2\times1+1,2\times2+1,2\times3+1,\dots\}=\{1,3,5,7,\dots\}.$
Indeed, at the top of page 7, the paper you linked says that $r$ has to be odd.