  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.

Classical Analysis and ODEs;Numerical Analysis;Numerical Analysis;Number Theory