A formula for the number of partitions of $n$ in terms of the partial Bell polynomials
Abstract
We derive a formula for $p(n)$ (the number of partitions of $n$) in terms of the partial Bell polynomials using Faà di Bruno's formula and Euler's pentagonal number theorem.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.01627
- arXiv:
- arXiv:2006.01627
- Bibcode:
- 2020arXiv200601627J
- Keywords:
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- Mathematics - General Mathematics;
- 11P81;
- 05A17
- E-Print:
- Accepted for publication in the Ramanujan Journal