summations with unusual notation,as interpreted? I have seen here and in many places summations that do not follow a standard notation, I put some of them below:
For example how to interpret these.
Some bibliography with this type of notation? I can't find anything other than usual

 A: The first does not appear to be a sum at all unless interpreted as on the right. The others also appear to be coded by people without a strong background in standard notation.
These are just educated guesses about what the coders intended.
\begin{align*}
\sum_{\large{r_1+r_2+\cdots+r_n = t,\space r_k \in\mathbb{N}}} 
\frac{t!}{r_1!r_2!\cdots r_n!}
\\ \longrightarrow\space
\sum_{\Large{t=r_1}}^{\Large{r_n,\space  r_k\in\mathbb{N}}} 
\frac{t!}{r_1!r_2!\cdots r_n!}
\end{align*}
\begin{align*}
\sum_{\large{1<t<k\le n}}
\ln\left(\ln\left(\sqrt[\huge{n}]{\frac{3n-2k}{3n+2k}}\right)\right) 
\\\longrightarrow\space 
\sum_{\large{k>t>1}}^{\Large{n}}
\ln\left(\ln\left(\sqrt[\huge{n}]{\frac{3n-2k}{3n+2k}}\right)\right) 
\end{align*}
\begin{align*}
\sum_{\large{k\ge0} }
(tk)^{k-1}\frac{z^k}{k!}
\quad\longrightarrow\quad 
\sum_{\large{k=0} }^{\Large{\infty}}
(tk)^{k-1}\frac{z^k}{k!}
\end{align*}
\begin{align*}
\sum_{\large{d|n}} g(d)
\quad\longrightarrow\quad 
\sum_{\large{\frac{n}{d}=1}}^{\Large{\infty}, 
\space \frac{n}{d}\in\mathbb{N}}
\space 
g(d) 
\end{align*}
