On Engel's Inequality for Bell Numbers
Morsbacher Straße 10
We prove that for all integers n ≥ 2 the expression
- Bn2 can be represented as an
infinite series with nonnegative terms. Here Bk
denotes the k-th Bell number. It follows that the sequence
(Bn)n ≥ 0 is strictly log-convex.
refines Engel's inequality
Bn2 ≤ Bn-1
Full version: pdf,
(Concerned with sequence
Received June 26 2019; revised version received August 25 2019.
Published in Journal of Integer Sequences,
September 25 2019.
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