THE RAMANUJAN JOURNAL, Vol. 3, No. 1 (1999), 45-54.

A Ramanujan sequence that refines the Cayley formula for trees

JIANG ZENG
Institut Girard Desargues, UPRES-A 5028 Mathématiques, Université Claude Bernard Lyon I, F-69622 Villeurbanne Cedex, France
zeng@desargues.uni-lyon1.fr

Received March 17, 1997; Accepted September 14, 1998

Abstract. A further combinatorial study of Entries 16 and 17 in Chapter 3 of Ramanujan's second notebook leads to a refinement of Cayley's formula for counting trees and generalizes the recent results derived by Shor, and Dumont and Ramamonjisoa. Our approach also yields a new proof of Clarke's extension of Cayley's formula.

Keywords: trees, Cayley's formula

1991 Mathematics Classification: Primary 05A05, 05A15; Secondary 11B83