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

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


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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