Journal of Integer Sequences, Vol. 12 (2009), Article 09.3.5

A New Identity for Complete Bell Polynomials Based on a Formula of Ramanujan


Sadek Bouroubi
University of Science and Technology Houari Boumediene
Faculty of Mathematics
Laboratory LAID3
P. O. Box 32
16111 El-Alia, Bab-Ezzouar, Algiers
Algeria

Nesrine Benyahia Tani
Faculty of Economics and Management Sciences
Laboratory LAID3
Ahmed Waked Street
Dely Brahim, Algiers
Algeria

Abstract:

Let p(n) be the number of partitions of n. In this paper, we give a new identity for complete Bell polynomials based on a sequence related to the generating function of p(5n+4) established by Srinivasa Ramanujan.

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(Concerned with sequences A000041 and A071734.)

Received January 3 2009; revised version received March 22 2009. Published in Journal of Integer Sequences, March 27 2009.

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