We completely generalize previous results related to the counting of connected Feynman diagrams. We use a generating function approach, which encodes the Wick contraction combinatorics of the respective connected diagrams. Exact solutions are found for an arbitrary number of external legs, and a general algorithm is implemented for this calculus. From these solutions, we calculate many asymptotics expansion terms for a simple analytical tool (Taylor expansion theorem). Our approach offers new perspectives in the realm of Feynman diagrams enumeration (or zero-dimensional quantum field theory).

中文翻译：

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连通费曼图枚举的精确求解方法

我们完全概括了以前与连接费曼图计数有关的结果。我们使用一种生成函数方法，该方法对各个连接图的维克收缩组合进行编码。可以找到任意数量的外部分支的精确解，并且为此演算实现了通用算法。从这些解决方案中，我们为一个简单的分析工具（泰勒展开定理）计算了许多渐近展开项。我们的方法为费曼图枚举（或零维量子场论）领域提供了新的视角。