Some formulas for Bell numbers

@article{Komatsu2018SomeFF,
  title={Some formulas for Bell numbers},
  author={Takao Komatsu and Claudio Pita-Ruiz},
  journal={Filomat},
  year={2018},
  volume={32},
  pages={3881-3889}
}
We give elementary proofs of three formulas involving Bell numbers, including a generalization of the Gould-Quaintance formula and a generalization of Spivey’s formula. We find variants for two of our formulas which involve some well-known sequences, among them the Fibonacci, Bernoulli and Euler numbers. 
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3 Citations

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An extension of Spivey's Bell number formula and its associated Bell polynomial extension is established by using Hsu-Shiue's generalized Stirling numbers and Gould-Quaintance's new Bell number formulas are extended.
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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…
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