By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are obtained. Based on these results, a new method is proposed for calculation of partial Bell polynomials based on prime factorization. It is shown that this method is more efficient than the conventional recurrence procedure for computing Bell polynomials in most cases, requiring far less arithmetic operations. A detailed analysis of the computation complexity is provided, followed by some numerical evaluations.

翻译：通过建立普通Bell多项式与有理卷积幂之间的有趣联系，本文获得了Bell多项式的若干组合与逆关系，以及数列卷积根的显式表达式。基于这些结果，提出了一种利用素数分解计算部分Bell多项式的新方法。研究表明，在大多数情况下，该方法比传统的递推过程计算Bell多项式更为高效，所需算术运算量显著减少。本文提供了计算复杂度的详细分析，并附有数值评估。