One possibility is to use my technique at How are big operators defined? to define \varsum, which takes the \Sigma glyph from the same font family and scales it to the size of \sum.
This approach has the advantage of using a glyph already in that font family. However, you may find the weight too heavy is the downside.
Note that I don't have the neo Euler font, so I demonstrate below with the eulervm package. After showing the \Sigma glyph on the first line, I then compare equations using \sum and \varsum in all math styles.
\documentclass{article}
\usepackage{eulervm,scalerel,mathtools}
\DeclareMathOperator*{\varsum}{\scalerel*{\Sigma}{\sum}}
\begin{document}
\begin{align}
\Sigma &= 0\\
(x+a)^n &= \sum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
(x+a)^n &= \varsum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}
\end{align}
\begin{align}
(x+a)^n &= \textstyle\sum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
(x+a)^n &= \textstyle\varsum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}
\end{align}
\[
\scriptstyle(x+a)^n = \sum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
\]
\[
\scriptstyle(x+a)^n = \varsum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
\]
\[
\scriptscriptstyle(x+a)^n = \sum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
\]
\[
\scriptscriptstyle(x+a)^n = \varsum_{k=0}^{n}\binom{n}{k} x^k a^{n-k}\\
\]
\end{document}

And here is a version that takes the \Sigma glyph in \scriptstyle by defining \varsum as
\DeclareMathOperator*{\varsum}{\scalerel*{\scriptstyle\Sigma}{\sum}}
It produces a wider result
