# 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.

## 3 Citations

Some combinatorial identities for the r-Dowling polynomials

- MathematicsNotes on Number Theory and Discrete Mathematics
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Recently, three new Bell number formulas were proven using algebraic methods, one of which extended an earlier identity of Gould–Quaintance and another a previous identity of Spivey. Here, making use…

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- MathematicsQuaestiones mathematicae : journal of the South African Mathematical Society
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Abstract In this paper, we consider extensions of Spivey’s Bell number formula wherein the argument of the polynomial factor is translated by an arbitrary amount. This idea is applied more generally…

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- IET Intelligent Transport Systems
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