Implications of Spivey's Bell Number Formula
H. W. Gould and Jocelyn Quaintance
Department of Mathematics
West Virginia University
Morgantown, WV 26506
Recently, Spivey discovered a novel formula for
B(n+m), where B(n+m) is
the (n+m)th Bell number.
His proof was combinatorial in nature. This paper
provides a generating function proof of Spivey's result. It also uses Spivey's formula to determine a new formula for B(n).
The paper concludes by extending all three identities to ordinary single
variable Bell polynomials.
Full version: pdf,
(Concerned with sequence
Received July 14 2008;
revised version received September 3 2008.
Published in Journal of Integer Sequences, September 7 2008.
Minor revision, September 19 2008.
Journal of Integer Sequences home page