Journal of Integer Sequences, Vol. 11 (2008), Article 08.3.7

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.

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(Concerned with sequence A000110 .)

Received July 14 2008; revised version received September 3 2008. Published in Journal of Integer Sequences, September 7 2008. Minor revision, September 19 2008.

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