factorial-sum 0.1.2

Efficient computation of factorial sums using a novel recursive identity

Factorial Sum

Factorial Sum is a Python library for efficient and exact computation of factorial sums S(𝑛) = 1! + 2! + 3! + ... n! using a novel recursive identity introduced by Abdelkrim Meziani (2025). This approach improves numerical stability, reduces recursion depth, and provides better performance compared to naive methods.

Installation

pip install factorial-sum

Usage

from factorial_sum import factorial_sum

# Compute the sum of the first 5 factorials
print(factorial_sum(5))  # Output: 153

Features

• Efficient algorithm based on a new recursive identity: S(n) = n² * (n-2)! + S(n-3)
• Faster than naive summation for large n
• Safe for large n using iterative computation (no recursion errors).
• Mathematically exact with Python’s arbitrary-precision integers.
• Lightweight & dependency-free (only uses Python standard library)
• Includes caching for performance
• Fully tested with pytest

Applications

• Combinatorics and permutation analysis
• Graph enumeration problems
• Factorial number systems
• Teaching recursion and algorithm optimization
• Benchmarking and computational mathematics research

Citation

If you use this package in academic work, please cite:

Abdelkrim Meziani (2025). A Novel Recursive Identity for the Sum of Factorials with Computational and Combinatorial Applications. [https://zenodo.org/records/16994879 / https://orcid.org/0009-0003-1849-4985]

Author

Abdelkrim Meziani